You should have abandoned sharing your list (hard to do after putting effort into it) and discussed why an evidential approach was better than their approaches at a philosophical level.

Eh, I'm fine with analytic philosophy. It seems like an essential toolset. The only sense in which an evidential approach seemed superior to me was that it felt less like cheating. I've encountered dozens of definitions of "God", and it's easy to pick a definition such that the entity necessarily exists or necessarily doesn't exist. Doing that and stopping there is cheating, I think, because it's not the sensus fidelium regarding what and who God is. Plainly Catholicism does use (by habit, not dogma) a small set of definitions of necessarily existing entities, but it's far from obvious that they are (or can be) the same entity, and quite dubious that those entities have much in common with Yahweh.