Hey Rio,
Seems like you and Dan are having a swaying motion type of vibration, interesting solution and thank you for working it out. I still think the upper plate will add rigidity to the structure, and seems like you have a very rigid set-up. I always was puzzled about only two supports on the motor cabinet, that you could get a lot of flex between the cabinets. Since I added the 2" square tubing braces between the cabinets, I mat not see it as much. The bases are built to a price point, but I agree that a more rigid base goes a long way to getting the maximum performance out of the lathe.
On the head stock alignment, would use a 0.0001" dial indicator to check the head alignment, then check at 0 and 6" with your test bar. I would the try the 4J and check the TIR at the chuck and then at ~6-8" out. As you can get some wobble with a chuck, I check that the wobble +/- around the 0 point is the same. Then you can do some test cuts with a two ring bar. Bed twist is more of a factor further away from the chuck, I set my machine up with a 0.0005"/foot precision level, running it the full length on the carriage travel. At 6" out from my chuck dialed in to better than 0.0001" at the chuck I get about 0.0004" total TIR at 6-8" out. This is similar to what Dan had. I then aligned the tailstock so it reads within 0.0002" of what I read at the chuck, looking that the sing is the same +/- around 0. There is a point of chasing your tail with all this, when you just need to say it is good enough.
Mark