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Had the same problem on my '35. The rear oil slinger had been installed backwards. Instead of slinging the oil back, it was pumping it out!! It's an easy mistake to make. The slinger is cupped and if you don't know better, you might assume it was designed to go over the rear main bearing.
If your tranny is leaking as much as you say, I wouldn't try to stop the leak at the universal joint cover...the oil will simply migrate back to the banjo and overfill it, leading to axle housing seal problems and ruined brake shoes. Better to stop the leak at the source.
By the way, you can't drop the tranny if you pull the rear end. It has to come out the top through the cab. Pretty straightforward job, though.