In a previous life, you were the chief metrology inspector in a tool & die shop, right? 
With length errors of 0.03% and angular errors of 0.01°, that machine is as good as you’ll ever get and better than most.
Based on what you measured on that square, I recommend not messing with the mechanical setup, because there is no way you can improve it and many ways you can make it much much worse.
The spot looks nicely round, so the next step will be to measure the actual kerf in various materials:
With that in hand, you’ll have no trouble matching the results @bernd.dk showed off:
Fire The Laser!