The only way event can interfere with convoy is if you miss a refresh as a result of an event that lasts quite a while. For example, if your convoy refreshes at say 7:42 on a sage day.

Fox usually don't last long enough for this to be a concern, you can control the time you do masuri/TI and can take breaks. quiz also doesn't last long enough to be a problem, you c*ually complete jinchuriki in less time than 20 min and you can control when you start etc etc.

AFAIK, the only event that might interfere with convoy is GNW and sage, and that's due to the change where cooldown became 20 min instead of 30 min, allowing an entire period to be fit into the events. And it's probably rare for GNW cause your land must be fighting and at that a long fight.

So really, you are exaggerating a lot....