tonearm mounting and alignment

You shouldn't be aligning the body of your cartridge, whether it's square or otherwise. The body of the cartridge doesn't trace the record grooves, so why align it?

You should be aligning the cantilever (ideally, the stylus, but that's too small to see). You need to align the piece that's actually tracing the grooves.

Yes, a better protractor would help you do this better. Search the forum archives. We've discussed the pros and cons of different protractors several times.

Doug, I appreciate the clarification. After searching through the forums, I realize I've been mounting cartridges poorly for years. I feel pretty stupid about that. I need a protractor. Do you have any recommendations?

I'm using DB Protract.
Its pretty clear and fairly easy to use. What you want is something that visually easy to align.

Another alternative is to get the Freckhart(spelling) alinement jig which is even more comprehensive.

Turntable Basics mirrored protractor.

Like Dan_Ed, I like the TurnTableBasics. Its mirrored surface with top surface image and bottom surface reflection make it possible to achieve far superior alignments than any non-mirrored protractor ever can.

That said, I'd offer two warnings:

1) getting used to using the mirror drives many people batty or blind, if you're not the patient sort it might not be for you;

2) the Rega arm, when mounted at the stock 222-223mm, was not designed for Baerwald two point alignment (what the TTB protractor is designed for). With most cartridges you should have no problem, though the cartridge will be well forward in the slots and slightly twisted. A few cartridges with very short stylus-to-mounting-screws dimensions might not reach the Baerwald null points. Low probability risk but worth a mention. If you have the capability to nudge your arm in to 219-220mm then you can align any cartridge.

G'luck, and there are no stupid questions!
Doug