I cannot but think that your aims will involve a lot of work, to achieve facilities that may see very little use.
After all we are talking hobby lathes, rather than industrial where time is money.
But don’t let me dissuade you!
The prismatic bed provides the alignment for the tailstock base, so that locking the tailstock assembly pulls it down onto the Vee.
Recently, i helped align a Tailstock where there was a clamp, but no adjusting screws to move the upper part relative to the base, for alignment. Lacking that feature, we used a G clamp to provide a screw adjustment, against a lightly tightened top to base clamp screw.
Having obtained the desired alignment, we then removed the tailstock and fully tightened the clamp screw, before rechecking the alignment.
On the mini lathe, such as the Sieg, (As on many other lathes) the upper part of the tailstock is adjusted by a grubscrew on each side, to move the upper part relative to the base. This was how I checked and adjusted the alignment on mine.
Having been given a quick release tailstock, (from another lathe,) found that it could not be aligned closer than 5 mm. Stripping the tailstock suggested that some of the machining had been done with an angle grinder, but that there was quite enough metal to mill 5mm fromone side of the lower half stop, to allow alignment on my lathe.
Having done this, all that was needed was a longer grubscrew on one side, to allow the centres to be aligned to within 0.0005″ (0.019mm) over a 13″ length, with the two halves lightly clamped.
Once aligned, the clamp was fully tightened, and alignment rechecked.
Howard