I use 000 grade grease in my gear box. It works very smooth and this grade of grease is one step away from a oil. Let it set for awhile and it lays out flat, semi liquid. The John Deere is 0 or 00 grade and works just as well.
The old time trick was to mix 1/2 and 1/2 gear oil and grease to make a thick semi liquid gear box oil.
Don't try a wheel bearing or normal grease gun grease, its way to stiff and will not flow back on itself.
As far as changing the seal with the shaft in place, just drill a small hole in the outer edge of the seal. Then screw in a small screw and use it to pull the seal out. You can buy new seals at any parts store, GM used the same one for many years, they should be in $5 to $6 range.
Use a socket or pipe to install the new one. They are small and bend easy if you don't get them started straight.
Joe