I very well could be wrong, and someone please correct me if I am.
But without seeing a schematic, Paul, I think you might be envisioning an elaborate band-aid that wouldn't actually solve your root problem.
So we have a motor, with a centrifugal switch, which enables the heating element only when the motor is running.
We have evidence of that switch being mechanically faulty - the terminal is loose.
The scorch marks and overheating also show that that switch is not in good health electrically.
Now, a secondary relay would offload the bulk of the heating element current... but you still need a way to trigger that relay to close. As we know, for safety, it must only close when the motor is actually running. (Not energized by the timer with *intent* to run, but ACTUALLY physically turning.). The source for this signal, of course, is a centrifugal switch on the motor.
See the problem? The very switch which would tell your new relay to turn on, is the switch you have shown is suspect.
You don't want to energize the relay from the timer's motor output, as a fault such as a seized motor would allow the dangerous condition of the heating element running without the motor turning. Likewise, you don't want to trust the relay control to the failing centrifugal switch, as who knows how it is failing mechanically, or what fault condition could cause it to close (or stay closed) when not expected.
I think you have no choice but to repair that original switch on your motor!