My old/factory presumed (bought the device from the original owner on Swappa) had a riser block that was somehow super-glued to the battery, that the ribbon cable for the coil sat on. The new battery (not used, purchased from iFixIt) did *not* have this riser block, nor did the coils seem to (I didn’t buy one of those, as there was nothing wrong with mine).
Figuring that it was just a matter of those contacts not being pushed into the pins, I opened it back up and found that the pins were indeed extremely springy.
Rather than attempt to get the riser off the old batter (as trying to scrape, like with a blade, something off a lithium cell didn’t seem wise), I just pushed the cable against the pins snugly, and used hot glue to cover/hold it, but not be taller than the surrounding heatsinks.
That was a few weeks ago, and my Qi Charging still seems to be working just fine. Hooray for laziness!