Recommendations for "fool proof" tool to measure between round surfaces

We make parts where we need to measure the distance between the OD of our part and a concentric circular pattern of pin holes/slots. We measure these at 0, 90, 180 and 270* around the part to confirm our pin circle is concentric to our parts OD. We are looking for the relative values between points (not necessarily a specific number) with a resolution of 0.0010".
Right now we use calipers and it works well enough but it requires some 'finesse' as they gently rock the calipers back and forth and look for the lowest value.
I'm wondering if there is a tool or maybe just a certain style of anvil that would make this process a more reliable by minimizing the person-to-person variability. I was thinking maybe a barrel shaped surface on the anvils? I see them on micrometers, but nothing with the range of sizes we need.

Holes are ~0.3125" diameter x ~0.4000" end to end, and the distance they are measuring ranges between 1.5" to 3.0" depending on the part:

The holes go through? Optical comparator.

Or a gage pin in the hole and a depth mic?

Tube thickness caliper? Round on one jaw, flat on the other.

Your expected range of tolerance is missing. I don't like suggesting instruments of questionable origin but a cursory search yielded only this (Insize brand at Grainger) besides a custom made gauge. Dimensions of anvil suggest it will fit into the slot. "Foolproof" suggests mounting the assembly on a Harig head type fixture, dialing the OD for concentricity, and checking with a DTI at required stops. This could also be done in the horizontal position with Rotab on a mill. The mic also requires some finesse but all other suggestions would entail more money and time to ensure "foolproof" inspection.

To the OP- As an additional comment, any variation in the slot lengths (one to another) is going to throw off your results. You probably already knew this.

This is what you want. Cheap and easy to take off anf put back on. I have had one of these for a couple of decades.

https://www.grainger.com/product/MI...Ki9jILxDeJ7EjdzCF6RoCgtcQAvD_BwE&gclsrc=aw.ds

This cell occasionally has new/inexperienced people running it so I need something that would provide a better feel for them when they hit the sweet spot. The narrow anvil on the calipers doesn't provide the best registration for newbies.
That ball tip looks perfect I'll have to see if we have any mic's that have the range, otherwise those tube thickness calipers look like they'd be worth a shot.
Thanks for the input guys!