Searching Google Books, I find only 25 results for "helping-adverb" and eight for "helping-adjective," so I'm not sure if they were so much abandoned, as such, but, rather, never very common to begin with.
"Adverb of degree" receives 5,500 Google Books results (major contrast with the above), so I would certainly say that one would be better off, in terms of likelihood of being understood, if one used that term rather than the one with "helping."
In terms of "credibility," I don't see anything particularly wrong, per se, with the use of "helping-adverb"—just a lack of currency. "Helping adjective," seems wrong, however, as English adverbs are defined in any current dictionary or textbook as modifying either verbs or adjectives, and hence "helping adjective" seems to make little sense because all cited examples would normally be classified as adverbs or adverbial phrases.
The idea of a "helper" word is, however, used in grammar sometimes; the Chicago Manual of Style, for instance, mentions "helper verbs." However, since all the examples cited above do pertain to degree, one could argue that "adverbs of degree" is more readily intelligible.
I don't think any term directly translatable as "helping-adjective" is commonly used in describing Japanese grammar, but Japanese is an agglutinative language, meaning that multiple word-like entities are frequently combined together to form what could be considered single words but that do the work of what could be a whole clause in other languages. To wit, Ikaserarezu..., whose basis is the verb iku "to go," could mean, in context, something like "Without anyone forcing him to go..." The various things added to the end of verb stems and then onto one another in turn are usually called in English-language descriptions of Japanese grammar "auxiliary verbs" or "helper verbs."
The rub: some of these "verbs" are conjugated as though they were adjectives: -yasui, as in yomiyasui "easy to read" (from yomu, "to read"), is exactly conjugated like, and functions as, an adjective. In fact, yasui exists on its own as an adjective in its own right, etymologically related though with a slightly different meaning. Hence, one might (though typically doesn't) speak of "helping-adjectives" in Japanese, and these do not necessarily have anything to do with degree.
Korean and Turkish are other agglutinative languages, so somebody familiar with them might have more to add on your last question.
The NP answer is correct. Your objections to it are no good. The Pandora's box argument doesn't make sense -- just because an adverb immediately precedes a noun and there is nothing else in the NP, this doesn't mean the adverb modifies the noun. That is what your argument assumes, and it is just not so. In such cases, the adverb modifies only the NP and not the noun.
Your other objection is that in many cases a given adverb cannot modify a NP. But so what? Adverbs can modify many things, and there are all sorts of restrictions and complexities. Just because adverbs can sometimes modify NPs, it doesn't mean that every adverb can modify every NP.
There is a refinement to the proposal that adjectives are modifiers of nouns that you might like to know about. In McCawley's TSPE (which gives a very interesting taxonomy of adverbs), it is not nouns that are modified by adjectives, but rather N' (N-bar). An N' is (a) a noun alone, (b) a noun with a noun complement (e.g. the P' in "the father of the bride"), or (c) the result of modifying an N' with an adjective, relative clause, or whatever. N' can be replaced by the pro-form "one", as in "The unbroken red ball hit the window before the broken one (one = red ball) did."
Best Answer