I was able to remove the pump from the dishwasher without having to remove the rubber pipes. 4 screws! This granted me access to the back of the chopper housing. From there I was able to remove the old chopper blade. Replaced the new one and reinstalled the pump to the chopper housing. The swap took less than 10 minutes. Reinstalling the dishwasher took longer than fixing the problem.
To ensure this problem never happens again, be sure to thoroughly recover all glass shards if a glass breaks. And to NEVER allow jars with labels run through the dishwasher.