Turns out that cutting out the (factory stock) rubber rim tape did the trick—the tire was tight but not un-unmountable that way. Thanks for the advice. You'd think after all this time, I'd know how to fix a freaking tire.
I've tried using filament tape as a base tape in the past and had trouble with it; I'm going to get some kind of flat base tape (Schwalbe makes one) and hope for the best.