Chosen Solution

With ifixit replacement battery in, the phone goes into a boot loop when the charging cable is plugged in. Without a cable it won’t boot at all. The Apple logo shows up for about 5 seconds and then it reboots. With the old battery back in, phone still works fine. Bad Battery, or is there a procedure I just haven’t found or read about?

That’s bad luck, a faulty battery behavior matches with the one you described, you’re not supposed to do anything else besides putting it in place and use it. Ask for a replacement, they’ll send a new one.