Messy smelly job! I replaced mine with Mobil 1 gear lube that had the additive already in. Not sure if you changed the crush washers but if not keep an eye on them leaking. Stupid expensive from GM but mine was changed under warranty for a leaking drivers side seal. The mechanic reused the washers and it continued to leak.
When I did mine I used a pump made for lower units on outboard motors. Worked will but just make sure the end does not come off in the housing. Nightmare. I kept the gear lube in a pail with really hot water, made it so much easier to pump the lube in when it was hot.
Think you need to drive in slow circles both ways to ensure the clutches are covered with the additive.
Glad you got yours done.