Hi James,
I don’t think Polaris is a good alignment star for Alt-Az telescopes. I have a fork-mounted Meade LX90, and Polaris is not in the list of recommended alignment stars in the handset. I vaguely recall trying Polaris in the early days and finding the 2-star alignment was less accurate. I think the other guidance is to avoid an alignment star when it is near the zenith (the tube is parallel to the forks) or below about 10deg elevation. Otherwise, provided the two stars are well separated in the sky then the Meade 2-star alignment is highly accurate every time (I use an illuminated cross-hair eyepiece to get the alignment star dead centre every time). I do spectroscopy with my Alt-Az Meade and using GoTo the target star drops every time into the field of view of my Alpy 600 guide unit.
Cheers
Hugh