I keep a few 12" long drill bits in the 1/8" to 1/4" range for just such purposes. I also have a the same dia bits in a 6" length. These are just too handy to not have around. A lot of my planes lately have been swapmeet planes that are in the bones or I just modify them to match my prefered setup methods. One of the problems with binding is that over the years you end up with a re-centering problem. Some planes dont care. But my Decathalon and warbirds generally dont like it.
Edwin