>I got both axles and all the nuts
> off the differential but it still won't budge.
You say you can't get the differential out of the axle housing? I'm assuming you've taken the axles out, and systematically removed ALL the nuts holding the diff on to the housing. Check again to be sure, particularly where the nuts may be hard to find. Usually you have to break the gasket loose by prying around the edges between the diff and housing with a screwdriver. If that doesn't work, try gently jacking under the diff to break it loose. It should come out, unless someone used super glue for gasket sealer.
Steamboat is a great ride. I went up three times when I lived in NM. You can usually get a package deal in one of the ski condos, and it includes tickets and pit pass. Definitely go for the latter. There were as many as 3 Alpines running some years, as well as some stuff that should be far too exotic and spendy to street race (300 SL Gull Wing, Bugotti, etc.). Lots of good times.
Good Luck
Rex Funk