PID controlling a heater to control its “surface temperature” is exactly equivalent to limiting the current through the heater. The easiest way to do that is not via a PID controller, but rather to intentionally “underrate” the heater voltage. For example, use a 240V heater on a 110V supply. Or wire two (or even three) heaters in parallel.
Of course, the chamber will take longer to heat with an underrated single heater… parallel heaters will help mitigate this.