Private purchase in Texas - need title for Michigan

Couple of questions/assumptions.

I assume you have a copy of the BOA letter, if not, get one.
I assume you have a signed bill of sale, if not, get one.
Are the “Texas plates” temporary ones you got while in Texas or the PO’s? Here it’s illegal for the new owner to use the old plates. When you sell a car here, the P.O. is obligated to turn in the tags to the DMV. But I’m sure not everyone does.

Yes it can take some time to get the title, one of the reasons you have 45 days to register it (Here anyway).