For some reason, every phone of this generation (2 years old) has had horrendous battery problems. The replacement battery for the 6p is only $18 on ammie, shipping from Canada. There's a reason for the cheap price.
Look at about 5 videos on how to do it. Each one leaves something out. Why do they do this? Because they want to sell you stuff. This is a difficult job because they use super glue in this phone. Next year, the phones will be solid glue, and try changing that battery! Applenose started this whole glue the battery thing, and I'm glad they are in big doo-doo with it.
I only had trouble with the glass thing at the top. When they say, apply sufficient heat, they mean lots of heat. I used a paint-scraper razor for separating things and that worked. Expect to crack that glass and start from the unimportant end. You can practice on that end. They are really vague on separating the case, use the razor, and go deep in a vertical direction. Keep your glass protector on.
And in other news, I was finally warm on my dog walk. My brown fat has finally kicked in and that only happens by freezing a lot.