I ended up going with Valvoline SAE 80W-90 Conventional Gear Oil, limited slip in my WH38X10002 transmission. It has been working well for the last 6 months. I am certain that I have vastly overfilled it with oil. I filled it until it came up to the bottom of the fill hole. I think it was somewhere between 16-20oz. Only later did I read in the technician's manual that this transmission came with only 4oz of oil! Again it seems to be running well, to my untrained ear.
Repair-man, 90 weight gear oil appears to be equivalent to somewhere around SAE 40-60 motor oil. Also from my reading gear oil should be non-detergent as a rule. I was also able to find some discussion about why detergent oil is bad in an unfiltered system
. Basically the dirt held in suspension by the detergent abrades the gears by acting like a lapping compound.
To share some answers I found to my own questions:
For the oil seal at the top of the transmission I found a TCM 06102TC-BX from Dichtomatik to do the trick. I had orderd it from MSC Industrial - 5/8 Inch Inside Diameter, 1/4 Inch Thick, TC, Automotive Shaft Seal
. I filled the inside of the oil seal with grease for installation. I did not look for a bottom oil seal, since the transmission held the oil I poured in. It must have been in good shape, since it hadn't been constantly attacked by the bleach and water leaking from the destroyed tub seal.
A note about the tub seal. I had installed a new tub seal for reassembly. The mating surface of the plastic tub looked good. The seal leaked! Luckily I came across someone who recommended Indian Head Shellac
. It worked like a charm and the tub seal has not leaked since.
What lead me to doing the repair was a growling transmission bearing. Its oil had been washed away by water leaking through a destroyed tub seal. I came across this great guide
to replacing the bearing on the so-called non-serviceable transmission! It was pretty quick and easy to access and replace the transmission bearing.