NavList:

Another option might be to shim the mirrors.  You could attach small pieces of stainless-steel shim stock to the back of the mirror where the screw tip bears on it, adjusting by trial and error with different thicknesses.  Once it's good enough, attach semi-permanently with a tiny spot of epoxy.  Grinding a wedge out of the back mirror surface is also possible.  Yet another option is to file the screw points, perhaps in combination with a shim.

I guess opinions differ as to restoration.  For working instruments, bringing them back to a working-as-intended condition doesn't seem bad to me.  Naturally, for priceless historical museum pieces one never wants to destroy information, and perhaps some violins fall into this category.  But for instruments intended to be used, making repairs would honor the original design intent, even if the repairs are invasive:  rebushing a hole, replacing a cracked shade, replacing worn fasteners or bearings, etc.

The reason I advised against drilling is that it didn't seem necessary from the pictures.  But since you say the pictures are actually post-rust-cleanup, let me flip-flop yet again: if the screws are immovably rusted, careful drilling, by a machinist, would be the way to get them operating again.  This can be done so precisely that the only thing left of the screw in the hole after drilling is rusted screw threads, which are picked out with a sharp point in a continuous, rusty helix.  Running a tap through the hole then cleans it up for a new screw.

For a sextant, the expectation is that the adjustment screws will work.  Shimming mirrors or filing screw tips is all very well, but it leaves a puzzle for the next owner, who then has to decide all over again what to do.

Cheers,

Peter

ps:  Frank mentions perpendicularity error.  Even that could be compensated for during sight reduction, since the error is a smooth function of angle.  You'd have to measure the nonperpendicularity to reasonable accuracy.