To step into the seller's shoes for a moment... I would want to make sure that the title company was a very good reputable company that was going to do a thorough search and I'd want to make sure that the buyer got an owner's policy.  If I am going to pay for the owner's policy, I'd also want to choose the title company.  Why?  Because I am going to be extending warranties of title.  If I could be held liable on the warranties, I think that is fair. 

If the buyer wants to choose another title company for their loan policy, they would be free to do so.  Of course, they wouldn't get the benefit of the simultaneous issue rate.

If that is not acceptable... I would probably not be inclined to convey title by General Warranty Deed - I'd use a Limited Warranty Deed. 

Best,
Robert A. Franco
SOURCE OF TITLE