Your situation is more complex than mine but here it goes.
I have had the same monitor for a 3 different desktop Macs over the past 4 years.
It has been without problems until about 3 months ago when it started blinking. No setting helped.
I then read that the HDMI cable can age and cause this problem.
I have replaced the old cable with a brand new one and the problem appears to have gone away.
Certainly simple to try.
Hope it works for you as well.
Bob