Tramming Super Spacing- What am I missing?!

I have a super spacer on my PCNC770s3. It came with the machine when I bought it used but I never used it because, well, I had to learn how to use 3 axis first!
I’m comfortable enough now that I want to use it but can’t get it square!
Using a dial indicator I have the face of the 3 jaw chuck square to within .001” min to max Y. I used a .005” shim at the front and got it square min to max Z. I then put in a precision 3/8” gage and along the ~1.5” it sticks out, my indicator doesn’t budge.

But then I start rotating things! I set the indicator at the center of the gage pin and zero it. When I rotate the A axis I’ll have a swing of about .010”! On a 3/8” gage pin! It’s a good McMaster one too!

Any suggestions? I feel like I’m chasing my tail.

Generally speaking a 3jaw chuck isn’t known for concentricity. Do you have a collet chuck or any other way to hold that Guage pin that would be concentric by itself?
This video from This Old Tony summarizes some of this. https://m.youtube.com/watch?v=K67bZQSETiE&pp=0gcJCdgAo7VqN5tD

I was aware that 3 jaws would have some play but I guess I just didn’t expect it to be quite this much! Good thing I have the 4 jaw too I guess.

I have been honing chuck jaws for a couple years and I still have no chucks that will grab something concentric. One thing that helps is if you tighten the chuck a little on each square hole until it’s tight. It helps but that’s probably still going to be +- 0.02
You could clamp some stock and mill it all the way around that should give you a round bar and remove any jaw variance.

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