Spanning 24" with 5/8 sheetrock seems a little far.

I'd me more concerned about the 24" than the 12" screw spacing

btw

code normally has some fudge factor built into it...

not necessarily, code making involves a fair amount of compromise & is
very dependent on the personalites invloved, some times it's just
worng, some times un-conservative, some times overly conservative

if code says x is enough, why does everyone seem to suggest using x+1?

because "the code is a minimum standard"........kinda like a doctor
who just barely passed med school.

For example, the allowable joist spans (esp for long spans) will yield
a floor that, for many people, is jsut too bouncy, but it's code. A

Put the extra screws in, you'll be glad you did. hink about about it,
if a screw fails the closest screws in one direction is 24" away, in
the other 12".

cheers
Bob