I'm wanting to use Armamentarium Complete + Artifacts alongside Fran's. There used to be a compatibility patch but it's grossly outdated, and doesn't have the updates to Armamentarium Complete.

One plugin, ArmamentariumLLMagic.esp, says it is not for Fran's, OOO, or FCOM, but it's the plugin that adds enchanted versions of Armamentarium's armor to the leveled lists. Is it so grossly incompatible that my bashed patch can't sort it out, or is it okay to go ahead and merge it?

I guess that if it's said that incompatible with fcom, it is incompatible even with the bashed patch.

Why don't you choose one or the other?

You can use it. From the Read Me "You can use the Vanilla Files in Franscesco but it will be unbalanced". From personal experience it works fine with bashed patch and tags.