Matt, Removing the Cardan cover on the final drive is very easy. Not even necessary to remove the rear wheel. You will need a fresh paper gasket when going back together. Hopefully, Lone Star will have one tucked back with the seldom called for Airhead parts...
With the cover off, it's another easy bit to lift out the spline cup and expose the bevel gear innards. Watch for and capture the large diameter shims and replace them as removed.
Kerosene would do well to flush out the final drive. You can rotate the rear wheel and inspect gear teeth although the bearings can only be checked via a full disassembly. There is also a large ball bearing that can be cleaned out and checked for scratchy racket. It comes away with the spline cup assembly.
As suggested, clean out as best you can, oil the big ball bearing, put 'er back together and don't forget to add the gear oil! Go for a ride and see how she sounds. If you wish, drain the gear lube again and check for fuzz.
Luck, amigo.