Learn English – “Who’s been waiting” vs “Who’ve been waiting”

Both options are perfectly acceptable. One is a noun-phrase (NP) complement of than and the other is a comparative-clause complement. They are structurally equivalent to

1. there is more than a budget cut
2. there is more than was included here.

In [1], a budget cut is an NP complement of than. Similarly, what meets the eye is also an NP complement of than.

(That's all you need to know about that construction, but if you want to unpack it a bit more, what meets the eye is like the thing that meets the eye. This is an NP with thing as its head and a relative clause functioning as a modifier. In the case of what meets the eye, the head and the relative are fused: the pronoun what functions both as the head of the NP and the subject in a modifying relative clause.)

The other option is there is more than meets the eye. In this case, meets the eye is a standard comparative clause functioning as complement of than. A comparative clause is different from a main clause in that it typically has a gap (e.g., I'm bigger than [she is _], in which the adjective big is gapped out.) The gap in your sentence is in the subject position (i.e., there is more than [_ meets the eye]) and could be filled by the NP the budget cut, for example, if it were a main clause.

The /bɪn/ pronunciation for "been" is I believe quite old. The Oxford English Dictionary says

The standard form been derives from the latter, and, in unstressed position, develops a weak pronunciation with shortened vowel in early modern English (continued as /bɪn/ and, in a less reduced form, as U.S. English /bɛn/).

Also, it indicates that spellings like "binne" and "bin" have been used as far back as the 16th century.

Even though "ee" is the standard spelling in present-day English, I don't think that the pronunciation with /ɪ/ is particularly stigmatized by most speakers, although I'm an American English speaker so it might have connotations that I am unaware of in British English.

For me, there are no exceptions: "been" is always pronounced /bɪn/, even when it is strongly accented for emphasis.

I don't pronounce "seen" as /sɪn/, and I can't think of any other word where I pronounce "een" as /ɪn/. However JeffUK pointed out in a comment that in some British English dialects, it is pronounced that way, particularly in the East Anglian and Norfolk accents. (30 seconds into this YouTube video)

The past participle of "do", "done", shows historical shortening of a different vowel: as far as I know, in standard British and American English, the only pronunciation that exists for this word is /dʌn/, or in weak contexts possibly /dən/.

The past participle of "go", "gone", also shows shortening, although in American English the quality is variable, and may be either /ɔ/ or /ɑ/.

The strong past tense (in modern English also used as a past participle) of "shine", "shone", is pronounced with shortened /ɒ/ in British English, but often pronounced with long /oʊ/ in American English.