I looked at a photo of your lathe. The headstock bolts to the bed. So if you rarely move the headstock, you can loosen the bolts, then shim to realign. That should address all "off center" issues. You still must be aware, as mentioned, that moving the entire lathe can result in twisting the bed. So that could re-introduce alignment errors. The best answer is to leave the lathe in one location once you have a good alignment. If the lathe tends to "walk" when turning unbalanced pieces, be sure to mark its location on the floor IOT return it to desired location where the alignment had been established. Also, a TS may be aligned at one point along the length of the bed, but not be aligned at another point. So take that into consideration when calibrating the alignment.
