PlanetsCentral

"Schedule change after a host run" doesn't make sense: if a schedule change is planned on Thursday, and host runs Wednesday 12:00, should I already change it? What if another host runs Wednesday 18:00?

On the contrary its perfectly sensible.

I totally don't understand you here. There is exactly one reason to do a scedule change - which is to prevent host from running. There is absolutely nothing else. The general reason for that is a player not present for a limited time, but even if there is another reason I can't grasp your problem.

The only reason to do a scedule change is to prevent the host from running. So if you did prevent the host from running change the scedule right away. This means you change the the scedule right after the hostrun you wanted to prevent on wednesday 12:00 if that was the last one you wanted to prevent. Which should in itself answer your secondary question.

So let's say usual hostrun is wednesday 12:00 but you wanted to prevent this one. Change scedule at 12:30 the same day. When the usual next hostrun will be at saturday 12:00 and that will be written in the game page.
Nothing else will change - there should not even be a need to change the auto checks. The host will still run if turns are in, and if there is a hostrun in that very time the hostrun at saturday will be delayed to next wednesday as usual because you want to prevent a host from running at saturday 12:00 when the last host ran friday evening due all turns were.

I really think that feature is what is causing so much trouble here because that's the reason for the host to run sometimes right after scedule changes and sometimes not. Which makes perfectly sense afterwards yet is practically impossible to predict.
(but naturally we want to keep that feature and just make the next host run predictable from the game page)