Have you tried running the server through the exact same process?
Client input → switch has auth[remote] → Slide → Srv RPC
Srv RPC: switch has auth[auth] → slide
The jitter is the server correcting the clients max walk speed. They are fighting each other.
Server is the authority. At n game time speed should be n. inputs/rpc’s have timestamps.
Here’s what replicated sprinting looks like. Should give you a bit of insight to changing/setting cmc movement speeds.