Actually, you MUST cool the P91 to below 200 F PRIOR to PWHT to allow complete martensite phase tranformation of the weld and HAZ. You want to finish the phase transformation, then achieve a tempered martensite condition with the PWHT. If you go from preheat directly to PWHT with P91, the tranformation doesn't complete and will occur later on cooling from the PWHT soak temp. resulting in untempered martensite.
Also, there is no problem with cooling the F22 or Gr. 11 to room temp prior to PWHT, or going direct from preheat to PWHT, whichever is desired. These alloys are not as sensitive for martensite formation as P91.
ASM Volume 6, Hardenable carbon and alloy steels, Postweld stress relieving, quoted "It is generally desirable to place the weldment in the stress-relieving furnace before it cools below the minimum preheat or interpass temperature"unquoted.
In ASME Section VIII, Div.1, UCS-56(d)(1), it specify the upper level up to 800F at the time of the pressure vessel or part is placed in a furnace.