NavList:

Rob van Gent, you wrote:
"Did you factor in the cos δ correction?"

Yes, but thank you for the reminder! Even ignoring the proper motion in RA, the proper motion for beta Hydri in Dec in Stellarium is roughly double what it should be. Is it actually wrong? Are they displaying it wrong? Are they possibly applying a factor of 15 or of cos δ backwards in the displayed values but not in the actual coordinate work? Is there some serious problem with their astrometry code?? 

This afternoon I looked at another case: the angular distance between Capella and Rigel and the change in that distance between 1 Jan 1821 and 1 Jan 2021. Rigel has nearly zero proper motion, and Capella's rather substantial motion is nearly due south torwards Rigel. So this should be easy, and all sources should agree very closely. Precession doesn't enter into it. Stellarium shows a change in angular distance of 1.47 minutes of arc. Better sources (SOLEX, USNO ICE, mine) show changes of 1.42 minutes of arc. That's close, but rather strange. Stranger still, the change in the distance in Stellarium does not seem to match the proper motion values in Stellarium! 

I should emphasize that I'm just poking around and reporting what I'm seeing after minimal experimentation, so double-check anything I have said here. 

Frank Reed