C-T-C distances can be frustrating......I'd be 100% disappointed engineering of that specialty caliper was not appropriately coupled with correct means to accomplish measurement.
Centering points on a caliper work well, provided attachment and 'calibration' are right. If you mic the OD's of said points, that adds a feature much like a Sorenson, with the same arithmetic.
Depending on hole size/s, drill blanks, pin gauges, dowel pins are reliably checked with outside micrometer or height gauge. Lacking the right sizes, a small pin clamped in height gauge works, if the part is perpendicular to reference surface. Knowing the diameters, arithmetic process is the same. Be mindful of edge combination used, or being a diameter off will seem correct. Yeah, I scale the distance first to predict outcome......
A mill can sub as CMM, once hole centers are parallel to axis of movement. Also an easy way to measure DBC of meshed gears. If not parallel, use X & Y and trig the solution. Without DRO, use travel indicators or careful axis movement to avoid backlash.
Another old-school way depends how you are equipped. Unbeatable when holes are roughly punched or flame cut. It's trammel points, hole centering balls and calipers with divider setting marks. Everything still available used online, except tin of deft touch and coupon book of patience.