Re-reading my post this morning it is a bit rambling so I thought I would summarise my thoughts.
The repeatability of the ALPY is good enough to measure a to wavelength precision of 1.5A given good technique (eg to detect relative changes in radial velocity in a given target) but an absolute accuracy of 1.5A is probably at the limit or perhaps beyond it without an external reference.
Even 1.5A precision can be challenging as many factors come into play at the sub pixel precision level. For example you mentioned the potential skewing of line profiles due to two or more stellar components. A similar effect can occur instrumentally if for example your star is slightly offset in the slit so the measurement is made on the downward slope of the star point spread function. The resulting shift in the centroid of the line can be significant at the sub pixel level. If high wavelength precision is specifically needed with a slit spectrograph then making sure the star image is significantly larger than the slit and even deliberately dithering the star across the slit can help. (fibre fed spectrographs have the advantage here as they scramble any gradients across the fibre aperture)
BTW did you take account of the intrinsic RV of the star (19.8km/s from SIMBAD) and the heliocentric correction which might account for some of the difference ?