I just wrote a little calculator based on Barrett's paper. It will let you calculate how accurate your PA needs to be given other parameters, including dec, guide star angle, and FL.
You can download it, and the source code in case you are a programmer, here:
https://github.com/133Parsecs/PolarAlignmentCalculator
There is a link to Barrett's paper at the bottom of the readme.
I hope it helps.
In general, 1 arc-min is very good. So good, in fact, I would question it if you just did a quick two star test. My experience is that two star tests often do not give highly repeatable results. I would try it a few times to be certain. And be sure to use different stars.
Also, the required accuracy will change as you go higher in dec, or change your guide star.
My routine is to try to nail PA as well as possible. Then I use a few minutes of drifiting in PhD2 to quantify it. From there, I plug the parameters into the program and see what my max exposure time is for each target I'm thinking about imaging.
Hope that helps.