Decades ago, a bike painter locally used to do this for clients as a way to personalize their bike. It is work, a jewelers saw will probably not be the answer as those are generally coping saws and there is no room for the saw frame really.
I would go the "Cinelli" or as seen on early Colnago Supers, a 12-13 mm did hole surrounded by slightly smaller, like 9 mm piercings.
There are some other things you could do depending on what is in the way such as cable guides and such