Thanks for responding, Jim. You've semi-confirmed what I was thinking, that the 135mm just doesn't have quite enough coverage to do the job. At your comment about using the 150mm wide open, I tried stopping WAY down to see if the vignetting goes away. It doesn't seem to. And print exposure times at those apertures would become far too long to be useful anyway.
Sounds like it might be worth trying a 150mm lens, to see if that fixes my problem. Anybody got one they'll let go cheap?