Customer, I have faced this problem many times in my Plumbing Business. What we do when this happens is we use an "Easy-out" bit such as you would use to remove broken bolts on automobiles after you drill a hole in them.
Easy-out bits are made in different sizes and tool steel. This makes them capable of being lightly tapped with a hammer so it will "bite into" the brass seat while at the same time, you have a crescent wrench on the head of the Easy-out trying to turn it.
So what you need is an Easy-out kit, crescent wrench, small hammer, patience and a helper. Push the Easy-out into the seat hole, have someone hold it while you put the crescent wrench on it, tap the head of the tool with your hammer and turn it at the same time. Keep trying this...tap it with a hammer and turn at the same time.
If this does not work, the only other way to correct this problem, in my experience, is to replace the shower body with a new unit. Obviously, this is a last resort.
I hope this helps, since this is what works for us.