Hi Jordan. When I "flushed" my transmission and transfer case recently, I drained the hypoid, and refilled with ATF. I drove it up and down the road a couple of times (shifting through all the gears), and then drained the ATF immediately while everything was in suspension. The ATF is very fluid, so it gets in all the small places and drains quickly (hopefully carrying much of the contaminants with it). You could repeat this process depending on how much stuff comes out, but I only did it once. I will likely drain it again this winter.
I wasn't in a rush, so I actually left the drain plugs out for several days.
Per the other thread, I refilled with Royal Purple (yellow metal friendly). My transmission and transfer case have been working very well... If not the same, they may actually work better with the Royal Purple (could just be my imagination)

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