Reflecting on some of the comments (thanks Timeshadow and Zzarchov!) and some of my more recent thinking about how I want firearms to work in my game, I'm going to revise my earlier rules for Firearms with the following instead:
Armor is less effective against firearms. Reduce a targets AC by 2 points, to a minimum of 9. Unarmored characters do not have their AC reduced in this manner.
Firing Multiple Shots
A character can fire up to 3 shots per round if their weapon permits it, making a separate attack roll with each shot.
All shots are against the same target unless the character is a Fighting Man with multiple attacks (eg. attacking enemies of less than 1 Hit Dice). If the character fires 2 shots add +2 on to the to-hit number, and if they fire 3 shots add +3 to the to-hit number.
Ranged weapons can fire a limited number of shots before needing to be reloaded. Any weapon can be loaded and fire 1 shot in the same round. A character may also spend their action for the round to reload all the ammunition for that weapon.
A character may not reload a firearm while moving, but they may use a Bow to move and fire in the same round. Characters may not load any sort of weapon, including a Bow, if engaged in melee combat.
Cover & Higher Ground
Cover adds from +1 to +3 on the to-hit number against a target.
Higher ground adds from +1 to +3 on the to hit roll against an opponent.
Short, Medium and Long Range increments:
Weapon Range Increment Tomahawk 10ft Derringer 10ft Shotgun 30ft Revolver 40ft Bow 50ft Rifle 120ft
+2 added on to-hit number at Medium Range
+4 added on to-hit number at Long Range
Note: If a character has a Telescopic Sight on their Rifle they only need to add +3 on to their to-hit number at Long Range.