I was thinking of Speed-Out (as seen on TV).  An attachment for a drill that is supposed to get any screw out.

I'd be patient before doing anything so drastic.  Concentrate on those screws; investigate other rust treatments, and remember, at the end of the day, they could be drilled out and replaced.  Patience, research and careful experiment is all.

KatLondon is correct !  Soak the platen screws with penetrating oil.  Remove as much rust from the screw slots with a small wire brush, screwdriver blade etc. as you can.  Find a screwdriver that is an exact and tight fit in the slot.  Place the screwdriver centrally in the slot and then hit the end of the screwdriver handle smartly with a small hammer (don't bash it, just give it a quick, sharp rap - once)  Try turning the screwdriver.  The penetrating oil plus the shock applied with the hammer may well jar the rusted screw threads loose.  If this doesn't work, you can sometimes loosen rusted threads using heat, locally applied.  But you do have to be very careful not to burn any surrounding parts/paintwork !