I do see this issue happening, but there's a slight problem of nomenclature here that's actually relevant to your problem: What you're using are pixel offsets, not pixel movement. Which is to say technically you do have pixel movement turned on, but you're not actually using it for the mob.

Pixel movement, to the engine, is defined as altering the step_x/y values. The pixel_x/y/w/z offsets are strictly visual. Thus the built-in glide code sees this strictly as tile movements.

I added features to the map to see how the movement works: a bunch of red turfs. What I noticed here is that your animation is all built around the idea that the player's mob will visually jump one tile at a time with no glide, because you've disabled tile gliding by including an object with off-tile bounds.

What I believe is happening is that because you're moving only once every four ticks because this is at 40 FPS, and therefore the client-side gliding code, although it's giving you a grace period to still consider the mob to be moving, isn't giving you quite as much of a grace period as you need. Slight timing differences between the client and server are enough to exceed that grace period. I can look into this more later on, but to be honest I'm kind of amazed it works most of the time, let alone all of the time in DS-only mode. This might be something I could fix by increasing the grace period.

What I did discover as a workaround however is that if you actually ditched all your pixel offset animations in Move(), and set world.fps to 10 while leaving client.fps at 40, the problem vanishes. Because of the nice even divisor, step gliding used to handle higher client.fps intervenes and you get flawless results even when hosting in DD.