Some tires are marked 75 PSI, some 85 PSI, some 95 PSI. But, those PSI ratings don't have anything to do with whether they would work with the obsolete rim style that JB has. Their bead must be designed for that type of rim to get a secure fit.
If two 27 inch tires have precisely the same width, they will deliver similar ride and handling characteristics at 75 PSI, even if one is marked 75 PSI and the other 95 PSI. The PSI stamped on the tire is a maximum PSI ratings, based on the assumption that the tire is mounted on the correct style of rim, and the correct width of rim, for a heavy rider. A lighter rider can ride a 27 x 1 1/4 tire at 10 or 15 pounds less pressure than a heavy weight rider and get good results, IF the bead and rim match.
I would have a good bike shop verify that the rims are in fact "smooth" and not the modern "hooked" rims. If they are smooth, replace them with hooked rims. A 700c rim, would allow use of any brand of modern road tire.