Oof, dog's breakfast...

I was going to suggest making sure the formatter board is fully seated into the socket on the mainboard, because it has some firm resistance when inserting it, but after that many tests you've probably got a good handle now on when it's actually fully seated. So that's probably not an issue.
Maybe the hardware and/or firmware are mismatched somehow, like maybe one of them is a wrong version for your printer, I dunno. When shopping ebay etc I sometimes saw parts listed for the wrong printer model.
Did you replace the mainboard already too? (the one in the metal box with the power supply) Asking because the service manual lists that as the first possible fix for error 01.1, and then the formatter as the second one.
Hopefully LPS can help out since you bought the formatter from them.
I don't think swapping drives between formatters will help. My understanding is a drive will only run with the first formatter it's installed on when new. After that initialization they are permanently "paired" and the drive will not work on any other formatter board (which makes drives from used printers useless). There's no undo so if the new drive inadvertently got paired with the old formatter during the swap tests, there's no way to make that new drive work on the new formatter, you'd need to get another new drive (as I understand it).
Your old formatter/drive aren't booting at all, but the new pair is, so that seems to be progress. Maybe it needs the new mainboard.