The cap would not move in any direction - up/down, back/forth, clockwise/countercw. Finally I got a rubber mallet and bonked it twice (along the 6/12 axis). Then it came off! Of course, at that point the cap might finally have been ready to come off. So I'll never know if it was the freezing, the WD-40, the rubber jar tool or the mallet bonk which convinced it to loosen.
When looking at the cap, we turn it counter-clockwise to fasten it. When doing that, the cap seems to go a little further in the counter-clockwise direction that I would normally expect. So I don't know if this is due to this particular cap being a little "out of spec". Or perhaps something, say the helicoid F-mount, has cut into the plastic, made a groove of some kind during rotation of the cap which might have caused the cap to stick too tight.
The screw-stop on the helicoid (opposite the mounting dot at 6'oclock) does not seem unusual in any particular way. But I don't have a way to know if it perhaps protrudes too far.
Anyway, all's well that ends well.
Thank you both for your help.