easy outs kind of suck, the taper is too short and they strip and don't grip well, I've found other ones with a better taper at the hardware store that have worked when easy outs fail.
use a center punch, and then drill it a little, reverse the drill and just the bit may get it to spin out … put some penetrating oil on the bolt, so the threads will let go of their grip.
your only real risk of damage is hitting the threads, but if you drill carefully, you should be good. It would also be a decent idea to chase the threads on those with a tap if/when you get it out. I'd just do them all if you do it to clean them up and keep things consistent.