I don't know what is the stock cap pressure spec.
The older cars did use a separate thermostat, so it may be possible to replace thermostat units. (At some point - maybe 1995? - they switched to a pcm-controlled switch as a function of sensor voltage.)
Are you sure that you are not just filling it to the warm line?
It's been awhile since I sold my last S car. But I think that there should be 2 lines: one cold level and one warm level. If you fill to the warm level when cold, then as it heats up and expands, then it will overflow...

Sorry for the stating the obvious...