I'd wager you could improve your current gloves. Have a look at this article:
http://uwnmbl.engr.wisc.edu/asb2010/abstracts/177.pdf
You could put 1/8" thick moleskin, the heavy stuff, right on your hands as shown in this article, then carefully pull your gloves on over it. You might be able to find something like that in a drugstore. You'd need a pair of scissors. This would totally be worth experimenting with.

More info:
http://www.sportsinjurybulletin.com/...-injuries.html
Here's a flash animation that clearly shows the sort of padding that's recommended:
http://www.specialized.com/bc/micros...tions/fig2.swf

I was wrong about the time off - they say 2-4 weeks to get better, some say 6-8 weeks. I think the idea of taking NSAIDs might be a good one. Reducing inflammation should also reduce pressure on the ulnar nerve.