take the deck out. Not any better way to do it. while it's out, you can clean underneath-they get dirty and the transmission dont' have no cooler, just the fins on the transmission itself with a fan blowing air over it, just like a BX tractor. Degrease it while you have the deck out. Also while the deck is out, you can change the deck gearbox oil and grease all the fittings that you can't see with the deck under the tractor.
you can do it with the deck still on it but you'll fight yourself, and if you're like the other techs I worked with, invent new words. That was always interesting. Personally I like to work smart, not hard.
When I get one of these dinosaurs in for service, I give customer the option to pay a little extra labor for me to do all that and then a little more, or do it the cheap way. 80% of the time (or more) they want it done right. You can tell who is proud of their equipment and who isn't. I used to own one (G1900S) and got real familiar with it. 1300 hours when I sold it. I didn't want to sell it but a guy made me an offer that I'd have been really stupid to pass up....plus I had another/newer mower already. But I still miss some things about the G1900. 5 gal of diesel ran all season with it. This newer mower? I've put 20 gal of gasoline in it already and probably have a month & a half of mowing season left.....not counting leaf mulching in Nov/Dec assuming it's not too wet.
insert a screwdriver or pry stick in the rear u-joint and let it spin against the frame, then whack the 12mm wrench to bust it loose from the flange on the engine. Rotate engine using your prys on the back, repeat two more times. Reinstall the same way, use some thread locking agent on them.