Both of my A units wobbled noticeably when run on our club layout. I don't run these engines on my home layout, but testing them here and paying attention to the behavior did show them to do the same thing here, so that eliminated track issues as being the cause. My first attempt to fix the issue was to tighten up the lock nut that holds the gear tower on the frame plate. Of course, if you make that too tight, the truck won't turn smoothly. It had a very slight effect, but the wobbling was still noticeable. American Models has an advertisement indicating that their wheels can run over a dime on the track and the wheels spring back. That feature is implemented by a small spring in the gear tower under the wheels (you can see the springs in the background in the photo). As an experiment, I removed those springs (they are seated in a small hole in the gear tower halves, and pop right out). However, that caused the axles with their gearing to sit too low. I built a small shim by gluing two 2"x3" scale strip styrene pieces together so that they formed a 4"x3" block. The spacing needed is 3 scale inches, so the block is laid flat on the 4"-wide side.
It is important to have the square bushings on the wheel's axle wind up flush with the top of the gear tower, which is shown here in the side closest to the camera (the one in the back had popped up a bit). When I put the side frame assembly back on the gear tower (and did the same adjustment to the other truck), much to my surprise I found that the wobbliness was gone! So, if your American Models engine has this problem, try replacing the spring with a shim block of styrene and see if it solves it.