Headstock is a separate piece from the bed. "Alignment" is keyed to the far side v-way, and the headstock is clamped under the ways fore and aft.
I'm gunna start by suggesting that you try to fix the worst of the worst first knowing it won't be perfect.
Assumptions:
1. You can borrow a precision level and maybe get someone to help you un twist your bed.
2. The stand is what it is. You are gunna use it as is and take the good and bad however it finds you. A new stand is a future improvement.
3. That spindle bar you bought is reasonably concentric. Even if it isn't perfect, it can be used.
Begin by measuring and marking the concentricity of the test bar as is. Just find the runout and mark all the high spots say every 2" from the spindle nose out and write the high runout at the high spots wherever they are. Then leave the bar installed.
Untwist the bed using a precision level and Shims at the bed bolts.
Use the closest and furthest high spots on the bar to align the spindle using your choice of shim material. Try just moving it before shimming it. Front to back pointing is more important than up and down pointing. So fix front to back first and then up/down. Might have to interpolate to find the best average.
Align the tailstock as best you can using whatever method you prefer.
That should look after the worst problems so call it quits at this point.