My vote is with the Egg; too tight wraps. They can be a beast some times. You really don't want to do it all over again, so you try to pulse. Sometimes it works, most of the time it snaps. Not really worth the extra effort anyway. Still, next time may be different, right?
There's a certain "feel" to when the tension is right. The coil should be moveable, but not
too freely. If it feels loose and springy, it likely is. If it's hard to move, it's likely too tight. You should feel a gentle "scratch" when you move the coil around.
Also agree with Vaslo to start with a weaker battery. Just remember to switch to a fully charged one after; to make sure your insulation can handle a full load. Been there, done that. Left the house with a new setup and a new battery - not able to fire up 4.2 volts without hotspots.
For the topmost wrap, there's a little trick you can try. If you wrap it a quarter-turn longer than usual - then unwrap it again, you'll get a nice, round "exit" from the wick. Instead of the straight line that tends to squash/push/dig into the wick a little. Problem with this "trick" is you may end up with a small gap instead of perfect contact on the topmost wrap. Do check
Edit: Completely unrelated: someone needs to make a gennie that clamps down wires instead of the tensioning screws we got now. All it takes is a square washer in a square hole.