I just took my first hot shower at home in a long, long time. The new valve (Caleffi 520) was a different configuration, so I took advantage of the opportunity to make sure that all three ports had a good straight run of pipe. I installed the valve and voila! everything is working perfectly. I can set the valve at almost the lowest setting and we have plenty of hot water.
Per Caleffi, the straight run shouldn't affect valve performance much--just make the flow less turbulent. So it sounds like I had two bad valves in a row. What are the odds?
I'm glad I embarked on this adventure: I have hot water, I learned a lot about how my system works, I have a cleaned and restored water heater that is performing to spec, and I replaced an Apollo valve that is no longer approved for domestic water! Thanks everyone for the ideas, patience, and help. This is a great community.