You can pulse the mover but it's not going to work as well as mover subclassing. You'll still get the jittery movement. I'm working right now on a redo of the map part posted earlier in the thread as a demonstration of how I would handle it. I'll edit this post as soon as I get done.
Edit: Ugh, this is a real pain in the ass. It's much harder to do this in UT versus U227. I'm not going to do all the background work to just make a useless demo but here's the steps...
Skip this part, it's better to use the next one
You'll need to find the mesh of the thing you want to make into a mover. In the demo map there are two Lightboxes on the front of the train. Using UTPT you can convert those from mesh to brush, then import that into the editor. Add your lightbox into the editor as BSP then convert that to a LoopMover. Replace the lightbox in the map with the LoopMover made to look like a lightbox and set it's keyframes and such to match the train. Do this for all the things you want to simulate as attached and they will all run perfectly together, no need to link any movers (though you could now and it would work).
One thing that bugs me though is that scaled sprites attached to movers don't work right for you. I did this in the MarioWorld map I was working on for Dane's PB gametype and it worked fine for me. I'm wondering if LoopMover messes things up where using a normal mover would not. I can assure you that multiple cycles ran on my map online and they never lost position but I used normal mover and not Loop. If this were my map I'd consider making the train identical on each end and running it back and forth on a trigger. I'll bet you the attached actors stay where they should be then. Perhaps in the moment that the loopmover begins it's cycle anew it loses proper replication sync to the attached actors? Don't know, but it makes sense.
Now I really want to know....Anyone running a UT server willing to test a map for me?