I have a drill press, and have done this before, but this one looks sort of fragile. Do you think it would be worth the trouble to dowel the existing holes prior to redrilling? Any other advice? I'll be drilling 12mm holes.

I think it's time for an upgrade.

Stupid question: Are you changing the style of tuner? Why are you reaming the holes?

The drill can be inacurate, and in some extreme examples split your head stock. Most people suggest using a taper reamer to increase your diameter.

Just looking really quick I found this one.
http://www.toolmarts.com/wood_working_accessories-ss4.html

Tapered reamers work fine. Use the reamer from both sides (obviously). When you are through using the reamer the hole is hour glass shaped as opposed to a cylinder. Then you must spend some time with a rat tail file to bring the sides of the hole parallel to one another and perpendicular to the head stock face.

Choosing tools for this job are dependent on the size of the existing hole and the size of the desired hole. If the new hole is only a sixteenth or so larger then using a hand held power drill is possible if you have a drill index. The drill index allows you to find a bit that just fits in the hole. Then choose the next size up. It will only be a few thousandths of an inch larger and will follow the hole with almost no effort. Do each hole and move up a bit size. It's a little fatiguing but is faster and more accurate than using a tapered reamer for someone with average skills.

After removing one it looks like maybe I should dowel the old holes and try to make the outside edge of the new hole in the same place as the outside edge of the old hole, IOW move the center of the new holes towards the center of the headstock. The new holes will be almost twice the diameter of the old ones, which are just over 1/4". I found a set of old Schallers on ebay which are smaller than most current tuning keys. The originals look like guitar tuners.

Glenn

If the new tuners require 1/2" diameter holes then plugging and drilling is the only way to go. Every other method will be long and drawn out with no advantage at all. Are you going to attempt to line the tuners up to get a straighter line from the bridge? Just curious.

That will be a side effect - my main concern is not having the hole too close to the edge of the headstock - you know how a lot of headstocks have little pieces glued on to gain width. I measured one of the bushing/sleeves and it was .472". A conversion table said it was something like 11.9998mm which is why I'm going to try to find a 12mm bit. Seems like most modern tuners use a 9/16" or 11/16" hole. I have no idea how old these Schallers are.

Thanks for all the advice.

Success - even added side dots. They're a big improvement.