I've come across this many times, on all sorts of applications and there's no one definate answer I'm afraid!!
Good pics, have you tried tightening it first? sometimes this works and is the first thing I try, then backwards and forwards, get some penetrating fluid on there. If it shears off, that might be a blessing!! We use a stud and bolt extractor made by Irwin which grips the head of the bolt even if it's rounded off and allows you to at least put a bigger spanner on it.
If it comes down to it you might have to cut the head off with a hacksaw, remove the lower unit and deal with the thread on the bench, hence the head shearing off would probably be a blessing!!