Is there any way for the "^assemblyname" to NOT show up on BOMs, short of using a new custom property for the displayed partnumber or setting the config to user specified name? This is going to make BOMs ugly. Hopefully, BOMs won't be needed until all those parts are made external anyway.
You can edit the BOM parameters directly in the BOM on the drawing. My suggestion would be to go through the BOM and edit them there, it is quick and easy.
Ok, maybe not quick and easy, but much quicker than trying to do it to each part file.