No harm done. You aren't the first person to do this.
I wish they would make the threads read-only after some period of time after the last post but...
That movement is from the inertia of the gantry and spindle head's mass moving and then stopping. That's where the heavier welded machines come into...
Yes, if the box slides smoothly and the slides don't have fine adjustment features then just shim the false front. You may regret using brads. Screws...
Thanks for the information Tom. It is always interesting to learn about the so many other things used for a specialized purpose that have "crossover"...