First, check your motor mounts. They are made with vulconized rubber sandwitched by two pieces of steel. The overall height is exactly 1". Generally they tend to compress and the rubber breaks down, this throwing off the alignment of the motor and spindle pulleys. I suggest you replace them and start there if you can see the rubber squishing out from sides beyond the width of the steel top and bottom. We stock these at $80 each. Use PN: MTR-0068. We ship internationally daily, so no worries about shipping. You can follow this link to order:
Fadal Parts Online
Just search for MTR-0068 and you can follow the checkout process from there.
As far as the spindle preload, you are correct. You can try taking the nose cap off and tightening the lower preload nut such that when you press the tool in/out button with an indicator zero'ed off the nose of the spindle, the movement should be around 3 to 5 tenths of an inch, or .0003 to .0005". You do risk setting the preload incorrectly and killing the nose bearings, especially if you have drawn in contamination from a faulty air purge system to the nose bearings. You just never know, but this should have been set properly by the spindle rebuilder and certainly not something you should have to address on the machine.
I've attached a photo of the motor mounts so you know what you are looking for.