Not a perfect solution I'm afraid, but a solution that works. For me.
I've custom settings on my LG27UK650 for brightness, contrast, warmth etc, which only has DisplayLink output. It played nicely with my previous Mac Pro (2012) desktop. I've recently moved to a Mac Mini and like others found the screen horrendously bright and the only option being to keep toggling the High Dynamic Range checkbox in Displays a number of times until the right mode sticks.
By accident I discovered a solution that works for me... I hope it works for you!
From a cold boot, let the Mac finish starting up until you are presented with the ultra vivid HDR screen.
Use the under-monitor control toggle to turn the LG monitor off.
Then turn it back on again.
Back to my chosen settings!
Tested on:
Mac Mini 2018
Catalina 10.15.6
LG27UK650 monitor