Interesting issue.

It had the locomotion tied to the head from the very beginning(your "entity rectangle" is moving together with your head), but I don't think it produced direct movements as "tilting left = continuously moving to the left, while head is tilted", if I'm understanding the issue correctly.

Sounds like you might possibly have some config alterations that are causing it. Did you alter mouse movement settings at some point? I think it might have roots in that, since VRMod can be "translating" certain things into GMod, as it doesn't have the direct grip on the game's engine.
Also I hope you're doing your tests with the rest of mods being disabled.