There are multiple runs of heater wire ( coiled nichrome, I think) encased inside the top of the press inside an insulating high temperature woven cloth 'sock'. Some of the weave material may be asbestos; take care not to make more fibes airborne than is needed; they are not healthy to breathe in.
I have an old Seal press and the screws on the top of it allow the top half of the top to be removed to get at the heater sets, although I have not had to service them.
I suspect you may have a short in the heater wiring so there is less resistance seen by the source, hence more heat.
It may heat some local section of the press faster than the thermostat can sense to turn it off.
The insulation inside gets kind of brittle from being hot for many times over the years.
I suspect some insulation may have deteriorated and broken away as the unit was moved or inverted to clean it up, and a partial short thus may have developed.
I suspect you are going to have to take the top off, and go at it with an ohm meter with the power off as a first step, to see if one of the runs is of a substantially different voltage than the others, and troubleshoot from there.
Be aware that the resistance of nichrome changes radically as it warms up. Don't take the cold resistance as being an indication of how much heat the thing actually runs at.