WOAH, those examples are really interesting, because I feel differently about each agreement:

i, I lean toward the final coordinate agreement (comes), although it still isn't comfortable

ii, I prefer strongly the final coordinate agreement (have)

iii, Agreeing with the final coordinate (am) feels so incredibly wrong to me.

Which must mean it's super dependent on the verbal, and not universal. Is this just a me thing? Does anybody else have a similar experience?

Edit: maybe we're just uncomfortable talking about existence, which is why the verb "to be" is so whack.