Shaking and alignment
Alignment of the shaft to the engine does not cause vibration of itself. If the reversing gear flange runs true AND the shaft coupling runs true to a straight shaft, it will not generate vibration. Aligning the shaft to the engine is a misnomer. The shaft is fixed to the boat by the cutless bearing and the stern tube. This is where alignment must start. With the shaft disconnected from the engine, position it in the center of the tube. This can usually be done by flexing the stuffing box hose up and down and sideways. You will feel the shaft hit the tube. Then approximate the center of all this motion and that is where the shaft belongs. Next you align the engine to the shaft - while keeping the shaft in its proper location. This is done by adjusting four motor mounts, any three of which will support the engine. You must assure that the weight of the engine sits equally on all four mounts, not easy. If any one of the top adjusting nuts pulls down on its mount, the loads of the other three are affected. To respond more directly to your post, every piece of rotating machinery has what is known as "a critical speed", where its vibration is the greatest. Balancing techniques can control the RPM at which the maximum vibration is experienced. Your vibration and a certain speed may be its manifestation. The shaft slapping the inside of the tube may well be because the shaft was not properly centered in the tube when the engine was adjusted. This has not ruled out defective motor mounts. Mounts are generally good until the rubber starts to take leave of the steel. This can usually be found by prying them about while looking at the interface. Again, if the load is not equally on all four, the mounting "system" can be considered defective. Consider too, these floppy mounts keep the engine noise out of the hull but what happens when you put that engine in gear and change throttle settings. Look at it!