Transcendental arguments ...

"Some argument is valid" (statement "V") must be a reliable move in any valid argument.

There are no reliable moves in an invalid argument (Duns Scotus).

Is it an axiom? Or is it a statement of the possibility of there being some axiomata?

What if we found that some some axiom A was (a) coextensive with V with respect to arguments or (b) was a necessary condition of 'some argument is valid' or (c) was a consequence of 'some argument is valid' but not of some other (independent) statement?

It's hard to imagine (a) being the case without this being a consequence of either (b) or (c), except that logical rules (symbol manipulation rules) look like possible candidates. Without them, it's hard to see how (b) or (c) could be demonstrated and there is some sense in which the scope of these rules is the same as the scope of valid argument (and therefore of V).

A logician might argue that V contains an undefined notion of validity, and so is 'meaningless'.

This is only the case if the definition is absent - not if it is simply incomplete. In a natural language, the concept of validity is both funtional and incomplete. Assertions of validity or invalidity may be stipulative ("This is the way we should talk."), or experimental ("Let's try talking this way.") But these stipulations and experiments may work or not work; and with them the language itself (if the breakdown is widespread) and so any possible concept of 'validty' at all.

Logic works with rules, but the language in which the logical rules are stated cannot be analysed as rule based.