Gtbarringer I would think that the overheating is a consequence of the electrical failure - if the SSR failed ‘closed’ (i.e. ‘on’ - they are not supposed to, but they do), then the element would stay on until something else broke the circuit: the element fails, the wires melt or the thermal cut-out intervenes.
I would think that checking the heating elements is a sensible thing to do in any case - even if they were not faulty before the overheating, they may be now… ; a 1 kW/110 V element should have a resistance of about 120 Ω