If you can get the Mityvac to pick up from the bottom of the diff, I think it should work but it could struggle with the thicker gear oil. I would try it with the diff oil warm.
Pulling the diff cover isn't a bad idea if not messy. I would go that way to avoid any drama. If you were planning on swapping diff covers to a Mag-Hytec or similar with a drain plug it's also a good time.
Pulled the cover to the rear. Gear oil was dark. But no shavings and everything was really clean. Put in 3 quarts of Lucas full synthetic 75w-90 and tightened everything back up. I think the front diff will wait for now since the rear was so clean. Too dang hot for me to be working in the sun.
I towed my 4k lb boat yesterday on a 50 mile round trip. I know this is nothing for a 3/4 ton truck but the lazer thermometer showed the differential running at 150 degrees in 100 degree heat. Looks like that Lucas synthetic gear oil does it's job. I was a bit concerned I made a wring choice if lubricants because it's not a very popular product as far as the internet is concerned.