Hard to say without seeing it but if none of the broken bolt is still sticking out, as in not enough to grab with channel locks or something, then it sure sounds like you'll have to drill it then use an EZ Out.
If you do bugger up the threads the problem grows. You'll still need to get the rest of the bolt out, then drill and tap the hole to the next size and use an insert.
If getting a full size drill in there won't work perhaps you can use a right angle drill and a mirror? It's likely the bolt isn't very tight, unless it is corroded, so you won't need much of a hole.