A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Roger W. Sinnott
Date: 2019 Mar 12, 08:59 -0400
Your methodology looks correct for a star’s mean place, referred to a given equinox, when you want to go from one epoch to another.
However, your position for Bellatrix on 2016 December 28 looks like an apparent place, meaning that, along with proper motion, the effects of precession, nutation, and aberration are included. Of these four effects, proper motion is by far the smallest. The others completely swamp it out, as you say, by 0.7 arcminute.