That’s a thou in real money – better than 90% of lathes out there I bet.

<p style=”text-align: left;”>Yes within a thou is actually quite good, considering the machine and age.  Carry on.</p>
Beware of those test bars. Some are notoriously poorly made and will give you false readings. You can do a basic test by placing it between centres and rotate it by hand. Check with a dial indicator that it’s running true at several points on both straight and tapered sections.

You are after all looking at a machine that is possibly over 75 years old and was not a world beater then, perhaps if you are looking to use small machines you might be better looking at Shereline/ Taig or one of the asian offerings. then you can use quick change tooling and an array of accessories not to mention a good range of spindle speeds.

Presumably the original alignment was out by the proverbial country mile in the horizontal plane?

The usual practical check, for alignment, is by turning a bar, at each end, and comparing the finished diameters.  An unacceptable result would indicate in which direction the tailstock needs to be adjusted.

Also conside that if the error of 1thou is at the tailstock end when the barrel is retracted ( and locked?) and just a short dead ctr sticking out then it could be a lot more by the time you add the length of a drill chuck and drill bit which could magnify the error 10 fold..

Doubt you will get much better than you have though.