This information makes a BIG difference!! If it didn't snap because it bottomed out or because it got in a bind then it shouldn't be "stuck" tight in the threads, making it easier to rotate. That's why I was suggesting to try and get it to move by tapping on it with a pointed punch and tapping on it "lightly" with a hammer. A tap extractor should break it loose pretty easy if it's not stuck in place. If you hit it too hard with a small hammer pieces will break off leaving you less to work with. But since it's in a "thru" hole it does make it easier to break up into pieces and remove each piece slowly. You can use a small (very small) chisel and a small pointed punch to slowly break it into pieces. The chisel and the punch will end up with some damage because the tap is hard but you can regrind the tools. The trick is to go slowly, take your time and remove pieces of the broken tap with needle nose, tweezers and a scribe. It's kinda like performing a delicate operation on an operating table. As pieces break off remove them or they will interfere with the operation. You might even (I've done this before) use some really skinny needle nose pliers by sticking the tips into the flukes. If it's not stuck it might rotate. If it rotates at all stop and put some lube in there to decrease the "drag" so it continues to rotate.