Piston I D

Depending on engine brand and model, the diameter is set somewhere from 1" above the bottom of the skirt to across the pin height and will taper as you go up on the skirt.

Your readings look like 4.058 near the bottom and 4.055 up higher. So I can't see this being 4.080 but 4.060", or .060" over for a 360 piston which has a stock bore of 4.000". So that hangs together with the 060 mark under the dome, and your recollection.

FWIW, if I were building and had a stock bore engine, I would go up the minimum possible, so as to leave as much meat in the cylinder walls for future rebuilds. .060" overbore for a 360 is a substantial chunk out of the walls. The extra cubes going .060" over versus .020" or .030" is pretty trivial, unless you are racing down to the nth degree and need every smidgen.