I used the RDM (Rollie's Dad's Method) to check the alignment of my lathe's headstock to the bed in preparation for the spindle upgrade. It was 0.003" 7.5" from the chuck, so not super great. I read about using shims between the headstock and the bed to adjust the alignment, so I gave that a try, but even the smallest shim I had (0.0005") swung the headstock way too far the other way. The problem is, any change I made at the headstock was multiplied several times at the end of the bed. I ultimately dismounted the headstock entirely and thoroughly cleaned the bed and headstock's bottom and made sure to get rid of any paint residue and other contaminants. I also filed the edges and corners and deburred the threaded holes. Once I mounted it back it was only 0.0005" out at 7.5" from the headstock, which is a number I can live with.
Ultimately, I think using shims to adjust the headstock would only work if it was badly out of alignment to begin with. Otherwise, I think taking it apart and clean everything thoroughly is the best you can do.