I expect an answer to your question will be difficult to come by. Many fish names form regular plurals (Bluegills, guppies, sardines), and many of the irregular plurals are fairly modern usages, so someone will have to account for the regular plural disappearing.

As You Like It, Act II, Scene IV. Touchstone says:

... and I remember the wooing of a peascod instead of her, from whom I took two cods and, giving her them again...

From The Sportsman's Dictionary: Or The Gentleman's Companion: for Town and Country. (1800) in a review of various rivers, one in particular:

well stored with gudgeons, dace, flounders, perch, pike, and some carp and trouts.

The American Fisheries Society has helpfully compiled a list of the proper plurals of fish names in A Guide to AFS Publication Style. Go here and look for Appendix C.

I started by trying to figure out the pronunciation of the second syllable. Here are the possibilities I can think of:

/tjuːs/ "tyooce": t + traditional English pronunciation of "long u"

The Oxford English Dictionary transcribes the pronunciation of plural status as "/ˈsteɪtjuːs/".

This is also the pronunciation recommended by the original Dictionary of Modern English Usage by H.W. Fowler, 1926 (as reproduced in the new 2009 edition) in the entry for "-us":

Many [words ending in "-us"] are from Latin fourth-declension words, whose Latin plural is -us (pronounced ūs); but the English plural -uses is almost always preferred, as in prospectuses.

(Fowler used the symbol "ū" to represent the sound /juː/, as described in his entry titled "Phonetics" where he defines it as the vowel found in the word "mūte".)

/tuːs/ "tooce": t + yodless "long u"

In some words from Latin, such as gubernatorial, people tend to pronounce “long u” as /uː/ (an “oo” sound) rather than the more usual English /juː/ (a “you” sound). (The use of /uː/ instead of /juː/ is regular for phonological reasons in certain contexts—after /dʒ/ or /r/, after a consonant cluster ending in /l/; after /t/, /d/, /l/ or /n/ in a stressed syllable in most varieties of American English—but I don't think any of these are relevant to the pronunciation of status.)

You can see from Greg Bacon’s answer to the linked question that tchrist equated statūs with "statoose", a spelling that suggests the English pronunciation /ˈstætuːs/ or /ˈsteɪtuːs/. The use of /uː/ rather than /juː/ may be in part due to a desire to more closely approximate the "original" Latin pronunciation associated with the letter "u", which did not have a palatal onglide.

This pronunciation is given in Fowler's Dictionary of Modern English Usage, Fourth Edition, by Jeremy Butterfield:

Many [words ending in "-us"] are from Latin fourth-declension words, whose Latin plural is -ūs (pronounced /-uːs/); but the English plural -uses is almost always preferred, as in prospectuses.

/tʃuːs/ "chooce": yod coalescence

A process in English called yod-coalescence ("yod" refers to the "y" sound at the start of "yes," written /j/ in IPA) has affected many words with the sequence /tj/. Before an unstressed vowel, this consonant cluster has changed to /tʃ/ (the "ch" sound of "cheek") for most speakers. For example, consider the common pronunciations of statute /ˈstætʃuːt/, stature /ˈstætʃər/, and nature /⁠ˈneɪtʃər/.

For British English speakers, I have read that /tj/ and /dj/ at the start of stressed syllables may be merged or near-merged with /tʃ/ and /dʒ/, although merger in this context seems to be less obligatory than merger in unstressed syllables.

This information suggests that for some people, an original /ˈsteɪtjuːs/ might end up being pronounced like /ˈsteɪtʃuːs/. However, I haven't found any references that mention this possibility for this word, so I am listing it as a possible pronunciation on a purely hypothetical basis.

/təs/? "tuss": closed-syllable shortening

Another complication arises when we consider the general rule of English pronunciation that gives a short value to a single vowel letter in an orthographically closed syllable (a syllable that ends in a consonant), regardless of the quantity of the vowel in Latin. For example, the Latin word jūs “law” was pronounced in Latin with a “long u” (/juːs/) but its traditional pronunciation in English uses a “short u”: “juss” /dʒʌs/.

It's true there are a number of exceptions to this rule in words taken from Latin; the largest class is words ending in -es /iːz/ (which includes many fairly commonly used plural forms of words ending in -⁠is, -⁠ix or -⁠ex, such as axis/axes, matrix/matrices, and index/indices). However, the pronunciation of -⁠es has another irregularity that adds some uncertainty: it not only has a “long e” vowel, but the final “s” is pronounced as the voiced consonant /z/, rather than as voiceless /s/.

I haven't found any dictionaries or usage guides that directly list an /əs/ pronunciation for the plural form "status". However, I found two documents that seem to indicate in an indirect fashion that this pronunciation has been used, by implying that the plural (and the singular genitive) of a fourth-declension noun is not distinguished in pronunciation from the singular (nominative) by most doctors:

In fact, there is a distinction between the -us endings above: in the genitive singular and nominative plural, the "u" is a long vowel (-ūs), whereas in the nominative singular it is short (-us). You do not need to memorize this, however, since you are not at all likely to see manūs in a medical document of any kind, and it is extremely unlikely that you will hear a doctor pronouncing the two words manus and manūs differently.

(The Hippocrates Code: Unraveling the Ancient Mysteries of Modern Medical Terminology, by JC McKeown, Joshua Smith, p. 131)

An older source also describes the genitive as being "like the nominative", which to me implies that the author would pronounce these forms the same way:

Latin nouns having the nominative in -us or -u, and the genitive like the nominative, are said to be of the fourth declension...*

(A Comprehensive Medical Dictionary Containing the Pronunciation, Etymology, and Signification of the Terms made use of in Medicine and the Kindred Sciences, by Joseph Thomas (1874), p. 669)

(Unfortunately, Thomas doesn't go into detail about the pronunciation of vowels in Latin words because, as he explains in the preface, in his time as in ours there was no consensus about how to pronounce the vowels of Latin words being used in English contexts.)

Of course, modern doctors generally don't possess any special expertise in the fields of Latin or English pronunciation, so you'll have to decide for yourself how much weight to give to this evidence.

The contemporary usage guide writer Bryan Garner wrote the following passage, which seems to imply to me that he thinks of the plural of such words as being pronounced the same as the singular (although I don't know how deeply he pondered the matter, or considered his wording—maybe "form" is only meant to refer to the written form of the word):

nexus. The acceptable plural forms are nexuses (English) and nexus (Latin). Naturally, the English form is preferable—e.g.: "The nexuses of activity for both rooms are the counters where the marijuana is dispensed." Glenn Martin, "The Tokin' Joint," S.F. Chron., 24 Aug. 1997, at Z1. Some writers have betrayed their ignorance of Latin by writing *nexi, as if it were a second-declension noun. (Actually, because nexus is a fourth-declension noun, it doesn't change its form in the plural.)

So this is another hypothetical pronunciation, but with some indirect evidence of possible use.

Pronunciation of the vowel in the first syllable

It may seem like the vowel in the first syllable would naturally be the same in the plural as in the singular, but this is not something that is absolutely necessary in principle: we do see vowel changes in the first syllable of the plurals of a few words from Latin, such as genus, genera, the anatomical terms vas, vasa, and (for some speakers) opus, opera.

And there actually may be a relevant rule that could lead to this complication for status. First, however, I will discuss the vowel in the singular, which is also variable in pronunciation.

Singular

As mentioned in the "Background" section above, the Latin pronunciation of the singular is thought to have been something like [ˈstatus] or [ˈstatʊs].

In English, the pronunciation of the singular form of status is always anglicized to a large degree (for example, the second vowel is always reduced to schwa), but there are different ways this can occur. There are two main variants:

• “STATE-us”, phonemic transcription: /ˈsteɪtəs/, phonetic transcriptions of some common pronunciations in various accents: [ˈsteɪtəs], [ˈsteɪɾəs]
• “STAT-us”, phonemic transcription: /ˈstætəs/, phonetic transcriptions of some common pronunciations in various accents: [ˈstætəs], [ˈstæɾəs], [ˈstatəs]. According to the American Heritage Dictionary, this has somewhat recently become the most commonly preferred pronunciation in the United States (their 1997 survey was the first to show this preference).

It is possible that some people use /ɑ/ (compare "data") but I would say that this is certainly not a major variant.

The use of /eɪ/ in the singular is in accordance with the general rule that a vowel letter in an orthographically "open", stressed penult syllable is pronounced long in English, regardless of its quantity in Latin.

Plural

Presumably, people who use /æ/ or /ɑ/ in the singular use the same vowel in the plural form.

The Oxford English Dictionary explicitly indicates /eɪ/ in the plural form status: /ˈsteɪtjuːs/.

However, I'm a bit doubtful about this, because it seems the rule for lengthening vowels in open syllables may have an exception for words where a traditionally-pronounced "long u" is in the following syllable (some examples: stature, solute, volume, tribute). Now, there are in turn known exceptions to this exception (such as nature), but it might be considered preferrable to minimize their number.

And for example, if someone already is accustomed to pronouncing "in situ" as /ɪn ˈsɪtʃuː/ or "genu" as /ˈdʒɛnjuː/, then using a plural form "status" that is pronounced /ˈsteɪtjuːs/ seems to introduce a certain inconsistency to the overall set of that person's pronunciations (or adds to that inconsistency, if it is already present).

That said, "in situ" and "genu" both have pronunciation variants with long vowels, which would be consistent with the pronunciation /ˈsteɪtjuːs/.

And it is possible that the tendency for pronouncing vowels short in a syllable before "long u" actually applies mainly to words with certain specific endings (in particular, "-ule" and "-ute") and not to all words with "long u" in the last syllable.

In any case, I can't find any source that supports using /eɪ/ in the singular and /æ/ in the plural of this word, so it seems like the best way to go is to just use the same vowel in the plural as in the singular (whether that's /æ/, /ɑ/ or /eɪ/).