Hold the Rx vertially against a speaker magnet, preferably a big musical instrument speaker. Rap the Rx well with the screwdriver handle. That will shake it up without marring it.
You might also hold the plastic tube from a can of WD40 or whatever, or use compressed air, against the weephole, and press the button. Maybe the pressure from the inside might push it out.
Once you do get it out, run the proper sized bit down the hole. My lower Rx drawings show the hole to be .097", and 1.25" deep. You should do this with a "pin vise" by hand if possible. If not, a Dremel tool on slow. Spray a solvent or something down it with a plastic tube tip to clean the hole out. Make sure you clean out the "weep hole" on the side afterward, too.
This is not a critical hole, as far as getting the size perfect. All you need is for the spring and detent to work freely in it.
I would not worry about hurting the Rx by drilling out, I would worry first about getting the detent out.