My original gear box had gaskets I made from very thin gasket material, I figured the thick gasket paper would crush over time and throw off the adjustments. If you do pull the cover, and reseal, be sure too re-adjust while you are there. I have had good luck with Anarobic sealer on greasy joints, they didn't get as hot as yours, but did seal good. Another good product is The Right Stuff sealer in the cheese spray cans. That stuff will seal anything and is really hard to get back apart.
Tractor Supply has the lawn mower gear box grease, very similar to JD grease, both are 0 or 00 grade, CV joint grease is also the same grade of grease and might take heat better than some of the others.
If you have had your gear box apart before, then you know about the steel spacer out on the end of the sector gear shaft. I removed that steel spacer and replaced it with a shortened bronze bushing that fit the housing and sector gear shaft, this took out a lot of flex at the end of the sector and pitman arm area. It's the same bushing as the box uses, only cut down in length. It also keeps the seal from leaking since the shaft is held tighter out the end.
Be sure to seal the threads on the side cover bolts, I think two of the four are through bolts in to the grease. I upgraded to the 1940 gear box for the roller bearings and slower gear ratio, it makes parking a lot easier.
Joe