Is there a way to restrict automatic statistics updates to a certain timeframe?
I would disable these auto statistics update and schedule a sql job to do on-demand stats update based on my defined rules, such as when the data change % is more than a threshold or when index fragmentation is more than a threshold.

Actually for big tables (100+ million rows), I always do this way because auto statistics update usually use a very small sampling rate for the big tables, and it often can cause more harm than good.