Finished the build, time to test...
Needed to check all the math is correct and the coil is performing correctly against a known magnetic field strength. Earth's magnetic field for my location is a good reference data point to check against. So dug out a regular hiking type compass to test, essentially making the Helmholtz Coil into a well behaved Tangent Galvanometer.
First issue was locating a magnetically clean environment in the building, bench doesn't cut it due to the pull out keyboard draw underneath with steel sliders, and I suspect the ESD mat contains some ferrous impurities due to the needle movement observed with the compass. These abnormalities were causing my initial bench top calculation of the earths field to be off by 3000nT (about 25%), so location location location. It's also possible I've been magnetizing these items with the Helmholtz coil and / or the magnets I've been testing the Aurora Observatory coils with.
Pretty much everything turns out to affect the compass, but I did find one clean spot, and yes the bench top PSU needs to be far away from the coil too due to the transformers inside :-) . On the plus side, the copper in the coil shows no residual magnetism (as it shouldn't), and the banana jacks also are good, so the coil is well behaved.
So the results...
Horizontal magnetic component for my location (i.e. magnetic north, also known as H; Bh; Horizontal Component) is:
Calculating the current to deflect the needle 45 degrees and -45 degrees, I get 599 and 651mA. Averaging = 625mA. 625mA x by the nT per mA for my coil from the openscad output for my coil geometry, I get:
This is an error of 0.37% (60nT), I can live with that when it's considered a mid strength aurora equates to a 100nT difference, and the Quiet Day Curve typically varies by around 30-60nT.
Method and Calcs to follow shortly in a YouTube video.