Some people pull the pinion support cover off and drain/suck it out that way. Others, myself included, go to the extra trouble of pulling the axles and third member to get it all out.
My reasoning is after trying to suck it out, drain it out, and otherwise fight with nature, it was much quicker to just pull the whole thing apart and be done with it.
That said... I now have a housing going in next week with a drain plug.;D
But my thinking in your case Matt, is that you might want to pull it apart to inspect your new gears for any funny business. Not that you want to waste an almost brand new gasket, but it's cheap insurance for finding any issues with a new setup now, rather than later. Or on a long trip!
Good luck no matter what you do. I'm frankly surprised that any lube-joint will have a tube small enough and a tech dextrous enough to get the lube out the fill hole, but then again, I don't know what kind of equipment they use.
Just make sure you watch their progress if you can!
Paul