Glad you found the source of your flexure. If screwed down tight I have found the ALPY to be remarkably stable. I could not detect any flexure on mine in tests moving at around the sky.
If you have not come across it before, Christian Buil has some information on the effect of combining lamp and stellar lines which you might find interesting.
Though not necessary for most applications, if you are looking for the highest accuracy using stellar spectra dont forget to take account of the earth’s motion and the radial velocity of the star which can add up to a few tens of km/s. The effects are small but can be an Angstrom or two, detectable even with the ALPY.