Boom Box!
Jim, as far as the noise goes.. it wasn't until the end of the production run of the 21 series that they had well or should I say, better insulated tanks. I have a late model KDS21M which is the Monterrey edition and the whole tank, top, sides and bottom are covered in a bituminous coating nearly 1/4 inch thick which is basically the same as what is used on the newer stainless steel tanks to absorb sound and vibration. The inner door is also lined with this material as well.
In additon, there is also a layer of fiberglass insulation for greater heat retention.
In your portable, they may have decided not to add much more than a thin fiberglass blanket since it was enclosed in its own cabinet.
Therein may lie your problem. The portable's cabinet makes a good box for resonating the sounds of the pump and water action.
If I were you,I would turn that unit over and inspect it to see what the level of insulation it has and then add to it and make the machine quieter by adding some more insulation. Unfaced fiberglass is easy to come by and use and since it is unfaced, it will not conduct electricity should it contact a live terminal.
You can add insulation to the inside of the door too to cut down noise as well as behind the front lower panels if none is there now. In the door, just cut away the area around the soap dispenser and the bimetal(s) as you don't want the dispenser door(s)to bind up or have anything get caught in the bimetal heater(s).
This has always worked for me and has cut down the noise considerably, but theya re still hurricanes in a box so it takes some work to quiet them down.
Let us know how you make out.