I would be surprised that you need different PID tuning requirements for each of the target temperatures. The tuning is usually just to get a stable response for the system as a whole (heating element power, system heat loss, system heat dissipation rate when turned off, etc. One set of tuning rates is probably the best route to go and then issue setpoint changes gradually if you want to slow down the ramping rate from one value to the next. So setpoint change managment might be a better way to go then trying to build in the ramping timing rate for each 'step' via PID tuning values?
Lefty