This afternoon I took the loom apart - I figured out how the shafts come out last night, so today I pulled them all out.  I went over each one; cleaned it with Murphy's Wood Oil Soap on all sides; sorted the heddles evenly to each side, and in the process took off and reset the ones that had been installed crossed; and waxed the bottoms of the shafts with butcher's wax.  Cleaned the plastic channels that the shafts ride on; cleaned the dust out of the bumpers with Q-Tips; Murphy-ed all the pieces I couldn't get to before the shafts were out, and oiled every spot where metal rides on metal.  Except the brake.  There are fairly hair curling warnings about not oiling the brake mechanism.

I put everything back together, and tested the action.  Everything moves more smoothly, the shafts are easier to lift, and it doesn't squeak any longer.

Now I need to clean the oxidation off the apron bars, and I'll be ready to go.  Funny how much work something free can be.  On the bright side, I know how my loom works and thats a good thing.  Oh - and the other bright side is that at the moment my sewing room smells like Murphy's Oil Soap and the solvent in the wax, which I find to be very nice smells.