I need help removing my broken water heater drain plug

I was removing it to winterize today and about 1/4 turn out, it broke off. I guess I tightened too tight before. I've had the same thing happen on my boat pontoon so I learned to take a drill bit and wallow out an indentation in a spot, being careful not to scarf the threads, so that my file can fit in the hole just right and have something to grab, as this never happens to leave any part of the plug where you can grab it with pliers or anything. Well, apparently, my boat plugs are not nylon because this technique wouldn't work with my nylon heater plug. I essentially could not get a groove going for an ideal catch point. I can't believe I couldn't get this to happen. Fortunately, this hole is slightly smaller than my pontoon, so my file grabbed the soft nylon when I shoved it in far enough. Boy, did it grab! I shoved inward forcefully so it wouldn't spin, but I couldn't get it to budge. Then, I but some locking pliers on the file to get leverage to rotate it. It held so strongly that I broke my file (it was a half round mf for those of y'all who remember the joke). It still didn't budge. So, I'm at a loss as to how to remove the rest of it. My best guess at this point is to stick a lighter in the hole and try to melt it away but I'm not crazy about the possibility of getting some melted plastic in the tank. Would the chances of that be minimal, since the drain is angled towards the ground a little instead of parallel? I tested burning the part of the plug that did come out with the head and it turns black and slowly melts. Any better or easier ideas? BTW, the head is 22mm which correlates to around 7/8" but I'm just seeing 1/2" plugs. Is that actually the same plug and the inner diameter is actually 1/2"? Thanks.