Are these wire bead tires?
When i got back into riding around 10-12? years ago, I was using a 70's Takara 10 speed with steel 27" straight wall rims and had no problems pumping the cheap Cheng Shin gumwalls up to 90 PSI. I do recall the tires being a severe PITA to mount though, so maybe the rim had a higher "wall".
I guess YMMV.
Remembered I still had the rims out in the garage-
They are ARAYA w/0? HP, so maybe they are "high pressure"?
The bike is now a 27 speed "hybrid/flat bar road bike" with CR-18's BTW.