Before you do any of these things, strip the wood off the metal parts and put some Kroil on the screws. Get some on the top and bottom sides if possible. Let it soak for several days using more Kroil as needed. This is creeping oil so it is best to put the part on an old cookie sheet pan or something similar.
The idea is not to break off a screw head or twist a bit to the point of making it let go. If it doesn't move after a week of soaking try a little heat then put on more Kroil while the parts are still hot. Let it soak some more. I have found that if you have to, it is best to flood the inside with Kroil if need be to get it on the inside end of the screws.
I also use the drill press method but with my minnie mill, it has a knotched spindle ring at the top and a wrench that matches. I tighten the shaped and sized bit into the chuck, line it up perfectly in the screw slot. Keeping down pressure on it I back the screw out with the spindle wrench. This is much more controlable than using a drill press. It is really important, especially with very thin slots, to make sure your bit fits the slot well and fills it up as much as possible. If the bit needs to be thinned just a little I found that an 1 1/4 inch diameter grinding stone slowly turning in the Dremel tool will be the right size to thin them with. Go slow and dip it often in water to avoid loosing the temper in the bit, it is easy to get the small thin ones too hot. Bob