Well, for measuring the offset, hopefully these pictures will help:
Since a calipers jaws are not a knife edge, measuring from an edge to a hole will always be slightly greater than reality. The smaller the hole diameter, the greater the error.
This is a board to represent what I assume you'll see in the end grain of your part.
Measuring to the inside edge of the (1/2") hole directly: Note, 2.540" Also need to have the calipers perpendicular to the edge (minimum distance).
Here is the same board on my router table circle jig. The post is 1/2" and this board was actually used on this jig so it's a "perfect" fit. This uses the dept feature of the calipers and the largish square shoulder on the calipers makes squaring up easier. Note, 2.538". A 0.002" difference. The last measurement is the one I'd consider accurate, but requires the fitted post in the hole. The first method is quick, just measure and done. If I was going to need to get that hole exactly 2.5" away from the edge, I know that I'll need to trim the edge back 0.040". If "close enough" was what I was after, I'd just use the first measurement, lop off 0.038" (or now knowing the error, 0.040") and done. So with this measurement complete on each end of you stock, measured to the same side, I now know that the greater number - the smaller number gives me the amount of material to be removed. With this known, I can then place the wood on the hinged sled with the planer set to just kiss the wood. Shims of the calculated dimension can then be used to lift the "fat" end up. The planer will then cut parallel to the hole. The part then can be flipped 180 and run through the planer until the distance of the hole matches. Since it is already parallel, that part is easy. Repeat the process from the adjacent side (90 degrees off) and you'll have a square part with a centered and straight hole. The pieces ends can now be cut square to lenght.
