syntax - What is and isn't a constituent, and how (whether?) can one argue that something is or isn't grammatical

Background

In CGEL on p. 1317, we find the following analysis of the sentence

[1] [Beauty] [as well as love] is redemptive.

They note that the singular is signifies that as well as is here not a coordinator (like it is in e.g. [Abstraction] [as well as impressionism] were Russian inventions.). In fact, CGEL says that in [1],

as well as does not form a constituent. This is evident from the fact that as well can occur on its own: compare Beauty is
redemptive and love is as well. In [1], then, the second as is a
preposition taking the NP love as its complement, and the whole PP
as love is an indirect complement in the AdvP as well as love.

This argument assumes that

[2] Beauty is redemptive and love is as well

is (for a lack of a better term---what is the right term, by the way?) a 'syntactic equivalent' of [1].

My question 1

Here is my initial attempt to formulate my question: what does the analysis used by CGEL say about

[3] ?He as well as they is going to L.A.

I'm putting the '?' because [3] sounds dubious to me. If [3] is to have any chance of being grammatical, as well as they must be interpretable as an AdvP (because if as well as is interpreted as a coordinator, then we need a plural verb: are going to L.A.). And if I'm following the reasoning in CGEL correctly, the AdvP interpretation would imply that [3] has the following 'syntactic equivalent':

[4] He is going to L.A. and they are as well.

This case is different from the one in CGEL because in [1], both beauty and love are singular, and so in the 'syntactic equivalent' [2] they both get the same (singular) form of the verb. In contrast, in [3] he is singular, but they is plural. So in [4] we must have the singular is for he, but the plural are for they. Given this difference, can we still say that [4] is a 'syntactic equivalent' of [3]? What is it that really matters when making this sort of an argument?

My question 2

What I would really want to do is present the following argument.

1. [4] is obviously grammatical.


2. [3] is a 'syntactic equivalent' of [4].


3. Therefore, [3] is grammatical.

I suspect that the answer is no---that there is no way to use grammar to predict whether some tricky sentence is grammatical or not. I would think that all you can do is this: once you already know (from analyzing corpora etc.) whether something is grammatical, then you can show that the reason for it being grammatical or not is that it does or doesn't conform to some rule of grammar. But 'rules of grammar' cannot help you with controversial cases. The only way is to know whether a controversial case is grammatical is to ask (a lot of) native speakers whether it sounds acceptable to them or not.

Is that correct?

Summary

To summarize, my questions are:

A. Is [3], in fact, grammatical?

B. In general, does the type of argument I presented above (1.-2.-3. in My question 2) work? In general, is that a legitimate way to argue
that something is grammatical? (Let's assume there are no idiomatic expressions 'anywhere near', i.e. that there are no relevant idioms that could complicate matters.)

C. This question is about whether it matters that both is and are are present in [4], but only is is present in [3]. Here I'm not really asking about the particular sentences [3] and [4], but rather about whether, when making the type of argument CGEL makes when it analyzes [1] with the help of [2], it would matter if the form of the verb in the 'syntactic equivalent' changes. Imagine there is a sentence kind of like [3], but indisputably grammatical, and also a corresponding sentence like [4]. Suppose that in the latter sentence there are both is and are, whereas in the former, there is only is. Does this fact, in and of itself, make it impossible to use the latter sentence for the purpose of syntactic analysis of the former (such as finding out whether something is a constituent of the former)? To put it another way: even if [3] isn't grammatical, imagine it were. Could in that case one use [4] to argue that as well as isn't a constituent of [3]? Or would this argument be invalidated by the fact that both is and are are present in [4], whereas only is is present in [3]?