Thanks guys
So it seems like this is what I have to do:
1- go to Michigan, hand over the cash, get the title from them in the presence of a notary
2- leave the car in Michigan, go to Ohio, get the new title in my name and pay sales tax and register plates.
3- get insurance
4- go back to Michigan, this time drive the car back to Ohio and get it inspected
Seems like an awful lot of driving and I wouldn't to pay them and leave the car with them, title or no title.
OR. In step 1, can I get temporary plates from the Michigan BMV, and drive the car to Indy?