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I think you are complicating it there. For a 1-roll system you can just do what I'm doing and use:
(Crit%*CritMod)*Damge + (Hit%-Crit%)*Damage
What this does is for your %crit multiplies the damage by the crit mod, then it takes and subtracts out your crits from your total hits and multiplies that % by shot damage. Or if you reverse the order maybe it would make more sense:
(Hit%-Crit%)*Damage + (Crit%*CritMod)*Damge
So it's how many hits will I get that are not crits, and then how many crits will I get. If you add up (Hit%-Crit%) and Crit% you of course get Hit%, and if you subtract that from 100% you get your miss%, which is in line with a 1-roll system.
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