This is what I use to cut the countersunk hole to accept the screws on a "new made" part. It may be possible to use one in a drill press, with the cord unplugged and turned by hand, to shave a tiny bit more out of the receptor hole to make the screw go on around to the next 12 o'clock/6 o'clock position. You would have to determine how much you had to work with before doing this. And, of course, it would not work if the screw head was filed to a contour to match the accepting part, as some are.
These are available in several different angles. I think the three in my set are 82 degree.
https://www.mscdirect.com/product/details/01051242 Best, SRH
