I see you state that not only are your screws rusted, some are broken off. I know they are small, but at this point I personally would get a small bit and try to drill them out. There have been time when doing this, the screws or bolts have actually come loose and began turning. Fortunately I was able to stop in time to be able to then back the screws out. I know it sounds like I have done this many times but I don't want to give that impression. Also, it hasn't worked every time. I was only trying to provide an option.
