Hi Seth,
Okay, on your phone the power button is on a cable with all the other buttons, which intersects the charging coil. I've had the bad luck to damage one of those cables on a phone where the battery stretch adhesive broke and I had to try and work the battery out with other methods. I can't say that's what happened to you, but it might be something to consider. The only way to check is to remove the battery again, and yes, I know exactly what a pain in the wazoo it is. Here's what the assembly looks like.
[image|3559513]
Anyway, as far as replacing it, I've already written everything you'd need to know about doing so in another question, so I'm just going to refer you there for now.
[post|794308|Power button replacement guide - iPhone 12 - iFixit]