I take it that this is on your F-150.
One thing I appreciate about Toyota trucks - there is a drain plug on the differentials, front and rear. Not only a drain plug, but a magnetic one.
In a situation like yours*, I cobbled together a Mercedes nylon vacuum line, which was very thin, about 1/8", onto the regular rubber line on my Mityvac, so that I could scavenge all the way to the bottom of the case and get all the old fluid. I would wait for warm weather, or hit the case with a torch for a bit, to warm the fluid and allow it to be withdrawn through that thin line.
*The transfer case gear on my wife's Volvo XC, known as the angle gear by Volvo, had the same issue. What a PITA to service it, and of course, it was a common failure point in that car. Junkyards have all been picked clean of angle gears, because they were "sealed for life" and hard to service, so, if you want one now, you'll have to pony up $1,800 for a new one from Volvo...
I emptied and refilled that angle gear several times, but when it started leaking from one of the seals, I pulled it out, re-sealed it, and added a magnetic drain plug... I wish I had done that a decade ago...sure beats scavenging it out slowly with a Mityvac.
Details here, if you're interested:
http://www.volvoxc.com/forums/showthread.php?29700-Angle-Gear-sealing-and-modification