JJMcGee83, if both tubes fit the GT Nano but not the Frog, it means that the Frog’s head has some issue on the threads.
Both my tubes (long and short) fit both heads. So I guess you received a damaged Frog head.
Even if the AAA tube didn’t fit the 10440 should fit so that you had a functioning flashlight (that is what one pays for)
Have you tried to contact the seller and explain the situation?
Also are you able to post any photos of the head and the tubes?
It ended up being the frog head. I got a replacement and that seemed to fix everything. Weird that the threads worked with the 10180 tube but none of the others.