It may be better to run a drill though the coupling and tap it put an m2 or m3 screw in for each side to lock on as an addition to clamp would be better than a shim but as that coupling is two pieces held together by a piece of rubber which is a just a friction fit I still think it may not be your problem and nothing to stop rubber coming away if ends stay in place. Check mill not slipping in collet and put a dial guage on top of acrylic to make sure not lifting seen acrylic do this many times, if using a bit with a helix try a straight router bit, also if it misses steps on upstroke it will get deeper. Anything movinng 3.75mm is going to be obvious so material or bit moving or missing steps sound much more likely to me.