In your case the easiest switch to find is a 10 amp 4 pole double throw toggle. Easiest receptacle would be a 4 pole 125/250 twist lock These are easily found at a Home depot. I can get you the remote, I've got a customer here with a pile of them, cheaper than you can get a rheotat for say $50 and shipping.

The only satisfactory place to mount the receptacle and toggle is on the right side cover

Exsisting 3 wires off the local rheostat goes into the top 3 terminals of the switch, center of the switch.
New wires need to run from the center of the switch back to the local rhostat, and 3 wires off the bottom of the switch need to run into the 4 pole receptacle (nothing to the ground terminal on the receptacle) Remember the codes for the new plug though, ie, x, y, z. so that the new plug and connectors can be wired identical, or make a picture.