Just because the tire is rated for 87 PSI, doesn't mean the rim can handle it. Older rims lack a hook that better holds the tire's bead. These rims may coincide with the 27"-tire era, but they are mutually exclusive specifications.

If your rims are indeed hook-less, then forget about getting higher-pressure rated tires until you get new rims that can handle those pressures.

What damage did you notice on one of the tires? We may be able to help assess whether it needs replacing. Better yet, post a picture.