Reliable system for constant movement along a track of parts

Hi, I’m part of a project recreating The Efteling, a theme park from The Netherlands. Our current project is creating a boat ride with constantly moving boats.

What I am now struggling with is trying to come up with a reliable system capable of simultaneously moving 14 separate carts all evenly spaced along a looping line of numbered parts that doesn’t impact the playability.

I’ve tried Tweens on both the server and client but both came with their own problems. Such as tweening on the server causing too much lag on the server end. Tweening on the client side ends up looking choppy and jitters a when in movement.

So my question is now, how would I go about making sure all 14 carts end up moving smoothly and in sync with all clients?