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What I do:
Get a bucket of really warm/hot water,
Set the diff oil bottles in the water to make the oil viscosity thinner,
Use a $15 hand pump from your local car parts store to pump out the bottled oil into the diffs.
Never thought of the hot water... Great idea, some of the gear oils are tough to pump!
This is a suction gun I used purchased from NAPA. Just need to mop it out between types of fluids. I tried a pump from O'Reilly that looked like a condiment pump... and that's all it should be used for. Didn't work so well. If you go with the NAPA suction gun, I would recommend getting a section of smaller diameter tubing that fits inside the tubing that comes with the gun for smaller fill holes and to add length which makes it a little easier to use. It worked great for filling the transmission.
I got the job done. I used an oil suction gun from Amazon. It worked pretty well. I put a 3/8 to 1/4 coupler on the end and it fit right in to the fill ports of all the diffs, and transfer case. Worked pretty well. The old oil looked pretty good, but I think I will change out after 15k miles just to see what it looks like then.
I’ll tough it out make something for next time. 
