Cyparagon, I find the force fitting method only works well for solid core hookups, and aluminum at that.
However, that method works to desolder the hole if its stranded copper, just requires you to strip alot of insulation. One benefit is that you have solder wick that, depending on your wire options, can fit in any hole.
I use one of two methods
1: If there is room to maneuver, then put a small dab of flux paste [not alot, just enough to break the tension] onto the hole and then with the wick placed over the filled hole, set your solder tip on the wick until the solder is "wicked" off.
2: Years back I bought a couple no name SS dental picks. Solder doesn't stick to them, and the tips are fairly sharp. For really cramped repairs, I would heat the hole from one end and insert the pick from the other. remove the heat and wiggle the pick till the hole is enlarged. Usually repeating with thicker picks does the trick.
If I absolutely need to have the hole fast, I typically drill it out. You'll need a drill press and something small, smaller than a 1/16, something like a #54 or #56 will do you fine. solder is very soft, won't need too much presure. Just know if you drill off axis you might cause irreversible damage to plate-thru contacts. Good news is that's easy to fix, just apply solder to both ends of the wire when you stuff it through. When in doubt, apply a little flux
Let us know how it turns out