Hi, Zapp.
Lets go back into history for a moment....
The oiling situation you have was an everyday normalcy for the folks who ran those machines back when they were new.......and were grateful to have them.....or have the pay-cheque for the job of running them, whichever.
Drip oilers are the obvious way to keep a Babbitt bearing alive, if kept filled and set correctly.
Yes, there may not be enough thickness of cast iron to drill/tap, so do as the old-timers did.
You can carve out a block of a good hardwood, such as hard maple, rosewood, cocobolo wood, etc, to the shape of your bearing cap, over the oil hole. Fit the hardwood block to the contour of the bearing cap closely, then cut a felt gasket from an old felt hat, and clamp the wooden block down snugly, using wraps of soft iron wire, or any other suitable method.
After the adapter block is fitted-up, but before you clamp it to the bearing cap, drill/tap the wooden block for 1/8 or 1/4 NPT, the hardwood will hold those threads nicely, and carry the oiler securely.
Placing the oilers in a central location, and running copper tubing to the bearings is even better, albeit a bit more work. As was suggested, enclosing the oilers in a neat, dust-proof hardwood box or housing would be an excellently nice detail, but make it glass-fronted so that you can observe the oil level in the reservoirs at a glance.
cheers
Carla