David, you might want to get to know a Preacher.
This is a device with three sharp prongs. Regard it as being a three pronged punch. You place one prong exactly in the location of where the arbor should be sitting and then orient the device to allow the other two to sit somewhere on the clock plate and then give it a sharp tap. This will leave two reference dimples that you can refer back to in order to verify your new arbor hole is in the correct position. The three prongs are usually set to have a uneven spacing so you cannot get the orientation wrong. You can knock one of these up in no time.
If the hole you are working on is really adrift you can use the Preacher to set the two references and then drill the arbor hole out completely oversize and plug it with a piece of brass. You then replace the Preacher in position and tap it gently once again to get a new centre in the plug to re-drill the arbor hole in the correct position. If you put a slight taper on the drill out hole with a reamer/broach then the plug can be tapered to match. The taper needs to be from the inside of the plate so the plug is being 'pushed' deeper into the taper by the arbor (in practice it doesn't move). Use a graver to get the taper on the plug. Overall it is quite satisfying process to do.
You will find that finishing of the plugged hole can be done to completely remove any witness marks that this remedial work has been done. Clearly you don't want to mark the plate surface when removing the excess of the plug that with even the best skills will initially be sitting proud. It helps if you have a piece of 35mm camera negative, punch a similar size hole in it to the plug and then glue it to the plate surface to sit around the plug. This will protect the plate until you get the plug pretty much flush.
I am sure Michael will be able to find you lots of references to Preachers and the process I have outlined.
Alan