If you run into this problem again just run by Publix and get some dry ice. Drop the barrel in it for 20-30 minutes and it may just drop right in, especially if you warm the upper a bit.I’ve had to heat a receiver AND seat the barrel with a plastic-coated dead blow hammer before.
You can’t heat the receiver past 225 degrees before you run the risk of damaging it, so you can only get it so hot.
You can run into issues where the barrel is designed to be thermal-fitted, AND it’s a bit on the large side of tolerances, AND the receiver is a bit on the small side of tolerances. In that case, you have the choice of forcing the barrel home, or swapping receivers/barrels until you get a “looser” fit.
I had to seat the barrel in that manner on my primary AR. Been running that gun for 2 years now with now issues. She’s accurate and reliable.
Now, it may never come out....