Another attempted solution:
Fearing that calling DisableMovement can cause disabling character position replication, I changed movement stop during montage method by implementing GAS attribute RootMotionScale and changing Character’s AnimRootMotionScale according to this attribute. When overlap event happens, instead of disabling movement, I apply a Gameplay Effect which sets the attribute to 0 and stops root motion.
For some reason it never worked with client overlap events so I had to check for them on server, so the movemnt freezing events became worse.
It still didn’t solve the incorrect position replication from server to autonomous proxy.