Consistent measurement down to very close limits is a fairly easy skill to pick up for anyone with mechanical sympathy.
Developing measurement set-ups using off the shelf equipment to do things that the makers never envisaged was a significant part of my work so I got pretty familiar with what is needed to coerce the right sort of behaviour out of things.
First, and most important, is consistency. Same result every time within the inherent accuracy and errors of the instrument. Consistently wrong can be sorted out later, fudge factor if need be.
Secondly, and closely related, is understanding what the reasonable expectations of accuracy are. Only way to deal with statistical variations is to make lots of measurements, which is no great help here. Even when I got paid for it I never liked it, try 500 measurements each on 1,000 data points with a reset needed for each one. In a dark lab! Computers have made things easier but there are subtle traps.
Thirdly, and the bit which most folk miss, is being able to see small variations. Which is where analogue instruments score. xxxx and half a line is a valid measurement so long as it is half a line width. xxxx and just over half a division is valid too, usually you can see the difference between 1/2 and 3/4. Digital devices are pants at this sort of thing. Flashing number rather than misaligned lines and no guarantee of equal hysteresis going both ways so error going up can be greater going down. Contrary to received wisdom digital devices do have backlash needing a certain movement to get all their numbers sorted out. With high end equipment you can ignore it because its all below the sensitivity threshold. More affordable stuff maybe not, something has to give when hitting a price point. Some of the early digital calipers were beyond terrible. Approaching 1/4" movement to get their counts in order. Great devices if you just wanted to close them down onto something in one smooth hit, not so good if needing to fiddle about. I still bought some and modded them tho'. There are good reasons why Newall stick with their fundamentallty analoglue ball scales.
However that said I'm inclined to think your troubles are more cut related. Itty, bitty, teeny weeny cuts are difficult. Unless the tool is uber sharp and dead on centre when cutting it will rub to greater or lesser degree in unpredictable ways. Slender boring tools need to spring slightly to generate sufficient pressure to start cutting. Which really doesn't help.
Best technique is to learn to trust your dials and make the last cut a cut. I usually reckon 10 or 20 thou is minimum. Take a cut, measure, set dial to read zero at final diameter and work down to it in reasonable stages. On a got to be dead nuts first time job there is much to be said for measuring two finishing cuts out make a finishing depth cut and verifying that yo actually got that cut. Adjust if need be. One sping cut should do the deed if its a touch small.
Clive