[DA] Extract duplicated logic from gcdMIVtest (NFCI) (#152688)

This patch refactors `gcdMIVtest` by consolidating duplicated logic into
a single function. The main goal of this change is to improve code
maintainability rather than readability, especially since we may need to
revise this logic for correctness (as noted in the added TODO comments).

I hope this patch is NFC, but I've also added several new assertions,
which may cause some previously passing cases to fail.