I didn’t read through this whole thing, but would love to dive in and work on this with you. I did 2-sided machining for a chess set and used pins. As I prepare to make more, I’ve been thinking of exactly what you did, as I think that locating on a square should be easier and more repeatable than pins, particularly on machines that deflect. I had a hard time getting a hole that fit just right, and I think it was down to taper.
Can you share the fusion file? Or message me and I can give you an email to add. I’d be happy to try this on my Shapeoko. I think you should have not problem doing this with the assumption that there’s no freaking way the Nomad is off by 1mm of repeatability!?
for a start, I’d suggest you touch off on your sqaure and ditch the bitzero entirely. Just jog over until you just see daylight disappear, then set your offset to 1/2 bit dia. For side on, do your facing operation. For side 2 just touch off against the wasteboard with paper or eyeball it. At the very least you won’t have 1mm of error finding zero!
Also, if you want to check the machine, you could clamp down a scrap piece, make a hole, power cycle, and see if going back still lets you jog in -z and have the pin fit like this method.
Share your file if you’d like me to take a look. I have high hopes for this method, but haven’t tried it yet!