Would It be possible to fit approximately 10 mm sandwich plate and not to use the original erroneous screw locations but make new ones furher away (and possibly Low Hex Head Screws or countersunk head screws)?
Maybe you need to make back fixing point trough the steady and sandwich plate, maybe there is enough space outside of the fixed steady?
This would allow to fix this steady to to sandwich plate first and then make fresh start for new fixing screws. Allows using the new (better and more locating postitions) for mounting and removing the fixed steady and allows better location fixing for news holes. I would put good size arbour between chuck and tail stock, locate steady fingers to near ideal places, CA glue the steady onto cross slide and then mark location for fresh screws.
Downside is that a sandwich plate moves the fingers away from the cutting tool, sometimes it is problem, sometimes not really that much.