Extending the range of calipers

[Toolmaker51]

I'm going to experiment with this, using parallel-jawed calipers. It shouldn't make a difference mathematically, but mechanically I wonder how relieved [pointed] outside jaws of a normal caliper interface in comparison.
I've detected variance before relying on Starrett master verniers as final word over digitals, those instances when only a caliper was available. It's far easier detecting proper contact perpendicular to cylinders or flat parallel sides, vice a narrow 'bite' of angled models. Overall, spherical contact is most effective

I'll perch caliper's spine on a pair of 1-2-3 blocks to establish that plane, easy part. The calculation could take me a week.
I need to figure a large radius, seat of a missing bandsaw table pivot, a 36" machine. It will take Tony Foale's version to measure. It's about 5"Ø, and dang near 180°. Have plenty of tooling balls, but no two in same configuration.

In lieu of that, will try a good-sized smaller cylinder and 3 gauge pins, starting with two of same size, third as a feeler. I expect greasing them, and a little manipulation so they 'find' centerline axis. Am I on the right track? Sounds like easy trig for a solution.
What attracts me here, the weight of sample will assure appropriate contact, quite close to the real thing, minus actual table. It is too big for casual handling, at about 34" square and 2.5" thick. Once the new cylinder is made, milling a flat, bolt holes and dowels will finish it off.