Jeeze, are old dishwashers really that loud? I have a circa 2012 "Ikea" (Whirlpool) dishwasher and I can barely hear it running. I took the door apart a month ago to replace the latch, and I don't remember seeing any insulation or sound deadening inside. It's so quiet I've found myself walking into the kitchen, 15 feet away or so, just to see if I remembered to hit the start button.
Either way, cool project! Glad to hear it worked out.
Oh yeah it seems the low-mid grade dishwashers never really had any merit in the sound attenuation department until prob the late 2000's early 2010's. I think improvements in the design of the water jets was the majority of the sound reduction, stainless steel interior tubs are supposed to be a huge reduction as well vs the plastic.
My apt before my condo had a 2015ish Whirlpool that was mid-grade ($500-600) and it was like yours where you had to be basically right next to it to hear a little splashing here and there.
Just to give you reference of noise, you know the commercial grade washers in restaurants and bars? Thats about how this dishwasher sounded before the sound matting.