I know that it's adding weight and possibly unnecessary complications, but if the problem only arises after a hot start, would fitting an auxiliary electric pump be any benefit?
Reasoning being, once the engine is stationary the coolant no longer flows, if the fan runs after switch off it will only be of limited benefit as a cooling aid. By fitting a small electric pump, coolant flow is maintained and there would, hopefully, be a decrease in the heat soak and less of a chance that there will be a pressure spike.
The auxiliary pump could be run by a controller very similar to a turbo timer. That way the length of time it would run for could be adjusted for the best results.
Would this work?
Is this a problem just with the K series? Or are other engines susceptible also?