@Gordo Can you tell us more about this "bounce/chatter" ?
How much hysteresis do you have set into your controller? See section 6.1 on page 19 of the manual ,
The copy I'm looking at is http://www.fujielectric.com/products/instruments/library/manual/box/doc/TN1PXRn-E.pdf
looks like default value is 1%.
It says
I'm wondering whether your "chatter" might be caused by the controller's responding to EMI interference introduced into the thermocouple signal by the act of switching 20 amps nearby...
Your short on-time during hold suggests very little hysteresis.
If you have none (or just 1%), try setting it to 10% and see if the chatter stops. If so, decrease it until you're at the verge of chatter and see whether temperature performance is still satisfactory.
Should you connect RC snubbers across the relay contacts be aware they'll pass a few milliamps through the heating element when relay is open.
So you shouldn't depend on the relay to place the element in a condition safe for touching it .
One should never work downstream of anything automatic anyway, remorseless robots that they are.
One other trick to try...
EMI is dependent on the area enclosed by the loop around which your kiln current flows.
For that reason it is desirable to run the two power conductors together and twist them , a turn every few inches will do.
That minimizes the area enclosed by them.
Do not separate them as would seem natural. Running them separately would make a big fat loop. You want a skinny loop even if it takes more wire.
Minimizing the area enclosed by the power wires will minimize the disturbance introduced into your thermocouple wire.
Also, route the thermocouple wire well away from the power wires and avoid running it parallel to them. Perpendicular is better especially when they're close.
Good luck !
old jim