Another observation here. It seems that cloth simulation might be the reason.
It worked randomly before as it wasn't turning off and on properly. Now it does and I started to get consistent results.
So I tinkered with all of the settings and narrowed it down to cloth simulation. When I turn it on, I do get that stutter if there are certain mounted troops in the frame regardless of other settings. It doesn't affect performance noticeably with infantry or some other mounted troops, but when certain mounted troops are rendered, FPS goes to like.. 3 per second?

Affected units are: Imperial Bucellarii, Aserai Faris, Sturgian Hardend Brigands, these what i detected so far in custom battles. I am currently testing other mounted units with hax in campaign to find out more.
What's interesting is the feature works fine with khuzait mounted troops: they even have distinctive helmets with plumes, and their the plumes do have beautiful cloth effects, but they don't cause stutter for me. So I guess stuttering units might be bugged in some way.
Caesar, can you, please, compare your stutter performance with and without cloth simulation in a full Aserai vs Empire 250vs250 mounted archers custom battle and share the result to confirm or deny my theory?