The working principle for the caliper is that the human eye can see the precise matching up of two marking lines more accurately than it can judge a position between two markings. So in fact, because the presence of symmetry is easier to judge than the precise amount of departure from symmetry, or put differently: zero detection is easier than measuring absolute magnitudes.
This fact is often used in technology, for instance by constructing differential amplifiers that can measure small signals more accurately than single-ended ones. But unfortunately it is difficult to use this advantage more than once. The ability of the eye to see accurate lining up of marking lines will not be increased by looking at the difference in lining up, if you just provide multiple lining up situations at different places in the viewing field. Just like triple-differential measurements - or amplifiers - will not immediately give you more accuracy than working just differential.
What may come closest to your proposal is the use of repeated inversions in time, like a "chopping amplifier" where the two input terminals are swapped periodically. This does cancel out most of the mismatch and makes it more sensitive to measure differences. So we then use time as the extra dimension.
Likewise, you could (optically, perhaps) provide the eye with a view of marking lines that should match up and where the image is alternately mirrored, say every second. That's a bit like how astronomers would compare night-sky pictures in the old days. Here it might make the detection more sensitive, meaning you can start with a finer vernier to begin with, and get a more sensitive total system. You will have to try to find out...
