A good and easy way to remove water from the housing is to use diesel instead of gas. Drain the housing and fill it with diesel then drive it around for awhile, DO NOT work the tractor, just drive it around. The faster you can go and more you can make turns to slosh the diesel around the better. The diesel will provide enough lube for the bearings so no worry there.
I do not know the oil you said you are using, in my 850 which is just a newer version of you NAA, I use UTF (Universal Tractor FLuid) from Tractor supply. It meets the Ford 134D specification or if you want you can use 80W90 in the transmission but most folks use the UTF because most of these old tractors have leaking seals between the transmission and hydraulic compartments. If they leak a little and you use the same in both compartments, no big deal. UTF is also safe for the differential compartment so one oil takes care of all three.
Your shifter is showing wear but not enough (IMHO) to worry about at this time. If it was trying to go into 2 gears at the same time then I would say replace it but right now I would not be concerned.