Kipi, you were right! What I thought was a monolithic machined piece is actually two pieces, and allows for some tilt. I cranked in a little up angle, and it seems a bit better - not so much weight on my hands, but could probably stand even more tilt.
I rode only about 10 miles today - I didn't get to start until early afternoon and it was VERY HOT! I cut my ride short because I was feeling the effects of the heat and was running out of water.
Anyway, the Brooks is feeling better and better. I'll ride it some more in about 10 days (leaving on a 1 - 1/2 week business trip tomorrow).
Here's a pic I just took: