I know that there are accepted practices in watch and clock repair that are certainly good enough to get the job done. There are also factors dealing with the standard watch and clock equipment that are traditionally used to repair timepieces. For example running a broach through a wallowed out hole in a clock plate as opposed to using a boreing bar. A BERGEON bushing machine broaching out a hole will NOT produce a hole that is as precise as a milling machine with a boreing head, however, it is good enough to get the job done and is a faster process. Drilling a hole with a two flute drill bit is less precise than turning an outside diameter in a watchmaker lathe. With a LORCH or WOLF JAHN lathe the precision is there and available (I am guessing you have one of these lathes from your shop picture) . Why not use it to full advantage. In my view as long as the pivot can be turned in the lathe as part of the final process you will get as much precision as the equipment can offer. I know that these views fly in the face of tradition but the fact remains that a turned part will be more precise than a drilled hole. If you have some spare time turn a pivot on a piece of solid bar stock, then, take another piece of solid bar stock, drill a hole in the end and press in a pivot. I contend that the piece turned from the solid will be a more accurate part. Watch jewels are probably the most precise components in a watch and they are manufactured by making the hole first, then turning the outside diameter of the jewel to the hole. The reason for doing this is to ensure the concentricity of the hole and the outside diameter.