Thanks!
I've since replaced the Federals with Veento G-2's. I thought maybe the Federals just had stiff sidewalls. Still size 155/80R12, load and speed rating 77T. They are slightly better but still too rough. The shop recommended 30-32 PSI, maybe 28. I suspect tire shops recommend a higher pressure so someone who never checks their tires won't sue them for having a blow out.
My old tires were the same size and did great at 32 PSI. Could it be the load and speed rating? The old tires had a load/speed rating of 76S, the new ones have 77T. In the US a load rating of 76 means a tire will support up to 882 Lbs, and a 77 up to 908 Lbs. An S rating means its good up to 112 mph, T up to 118 mph. I've read the speed rating in particular can affect ride roughness. Unfortunately all the 155/80R12's I find are 77T's.
Looking at newer cars with similar weight is an idea.
Then there's trying lower pressures until I get a decent ride - then monitor tread wear for under-inflation.