Thanks for the replies guys. On very close inspection of the freewheel cogs I could see the wear spots. Since this is an old freewheel with those very tall sprocket teeth I got to thinking maybe I could do something to them to fix this based on a vague reference that Sheldon Brown made to reconditioning such sprockets on his freewheels page. I could find no detailed information about how to proceed with such a repair online but I decided to go ahead and try anyway. I had nothing to lose since this freewheel needs replacing. I used the fine sanding drum on my dremel to go over each tooth and even out the spots where the old chain had been riding. I put the bike back together and rode it around for a few miles really mashing on the pedals. The skipping is completely gone. Now I can put in some more miles till I get those new sprockets.