ok465:
First time I saw this was way back in the 738 with a TOGA actuation on the left RF prior to the FROP performing the PSP procedure. On AP, aircraft reversed the turn direction to the right and headed for the Dino Martin memorial mountains.
AKA, Mother Sinatra memorial mountains.
Having said that, part of RNP AR training is not to go to TOGA until the MAP in the event of an early missed approach. Really no different than in any missed approach. Climb, but maintain final segment track to the MAP.
Some foreign countries are quite specific on the chart. At WAPP, for example, the chart states: "Missed approach transition to missed approach RNP for lateral guidance must not be initiated prior to the along track position of DA/H."