Thanks all, great suggestions!
More facts which may rule out a couple of mentioned items: 1) the tank has been thoroughly cleaned and lined with Caswell's liner, 2) the petcock is new (the old one leaked and was shot), 3) the airfilter is new and probably has less than 10 hours on it (and I do not live in a dry dusty area).
I'll remove the petcock and inspect the screen, and the screen at the carb, which is the stock one (Amal 620 or 647 - bike's not in front of me at the moment).
Now, I noticed Sunday that the carb-to-intake manifold looks wet in several places. I will change that part.
If water or condensation is getting into the carb, I wonder where the hell it's coming from? The bike stays inside when I'm not riding it and the tank filler o-rings are tight. If there is water in there, it makes sense that it blocks the main jet when the front of the bike is higher than the rear.
I noticed Sunday that it had more power going up the hill ONE time than other times on the same hill the same day. Maybe ignition then! I'll also check that.
Thanks all!