The problem here isn't with getting the device unlocked, it's with the IMEI.
Unlocking just lets you take the device to any carrier. It doesn't do anything to help you if the device is eventually blacklisted (and the blacklist is shared with your current carrier).
So…breaking the device gets you a replacement. Since Apple replaces like for like, guess what happens? They check the IMEI of the previous device and what do you know? Previous device is locked. So, you get back a locked device.
OK, now it's got a different IMEI but you're still back at square one. Because you have to get the carrier to unlock it. Maybe you get lucky and they don't cross-reference the new IMEI to the old IMEI (since this is a replacement) but you're still having to deal with the problem.
You may luck out and get it unlocked that way, but it's going to be a journey.