Cool info/history. Thanks. Some I knew some I didn't.
On the topic and relevant to the post:
It's a fantasy game unfortunately. Verisimilitude is important to a degree but I think the idea or flavor of firearms in a fantasy setting needs to be strong for them to have any reason to exist. Like you said the main reason firearms took off is ease of use. In an RPG that means absolutely nothing, every PC is already above average so how else can firearms be distinguished? Absolutely crossbows SHOULD be armor piercing but for balance they aren't.
I guess really firearms should be simple weapons.
Let's assume though that since this is a fantasy game and Golarion is a fantasy setting that the firearms there are stronger than what we know. Maybe the bullets are made of denser harder material. Maybe their form of gunpowder is even faster burning, I don't know. You get my drift though.
They need to be distinct from bows and I think the armor piercing idea at close range is interesting and different. I like it although I well know it isn't necessarily realistic.
It's annoying to sometimes err on the side of fantasy and sometimes not but I personally can let it slide in this case.
My means of handling guns has been to make them Martial (not Exotic, but they
are harder to use than a crossbow) give them good damage (D10 for pistol, D12 for carbine, 2d6 for musket), a 20/X3 Crit modifier, but a 50' range increment (30' for pistols). Like a heavy crossbow they take a round to load. The high damage and crit multiplier are because those big, fat, soft, slow lead balls are excellent at transmitting energy - bone does not so much break as shatter.
If I am using critical failure rules then a gun fails on 1-2, confirmed by a second failed to hit roll, much like the reverse of a critical hit. This is double the chance of most weapons. To make up for the increased fumbling I have been tempted to increase the X3 crit damage to X4, but only when using the chance of critical failure.
I have never had a gun explode on me, though I have had them fail to fire. And I have put several hundred rounds through archaic firearms. Keeping the guns
clean goes a long way to avoiding the failure. The guns I have fired most often have been Land Pattern (Brown Bess) - a friend of mine has one that saw a full century of service, first in the British army, then the British navy (where the barrel was shortened to carbine length and the muzzle flared), then to the Spanish navy, then the Spanish auxiliaries in Mexico.
In play they don't feel much like a crossbow or a bow, most often the players take the pistol as a close range weapon and use a crossbow at range. A six foot long musket is just plain awkward, though with the invention of the plug bayonet this will become an advantage, allowing the use of the gun as a spear. And since the bayonet was invented ca. 1611 and my game takes place ca. 1630....
They don't need special rules, any more than a crossbow needs special rules.
However, looking at the Pathfinder rules for firearms I am tempted to add a similar rule to the Broken quality to my own game - call it Fouled. If a Fouled weapon is fired without cleaning then it gains Broken if it misfires. If you are silly enough to fire it again without Repairing the gun and get another misfire, well... you had two warnings, eh? *BOOM!* (After a misfire I have
always cleaned the gun thoroughly. You are an idiot if you don't.)
I might even allow the 'Touch Attack' rule as a special ability for pistols - close range and aiming at things like the visor are a lot easier with a pistol than any other weapon. With a musket on the other hand... bleah.
That said... I like some of what I see, but feel that all three classes should be in setting books rather than a more general book on combat. I say this in spite of the fact that I am thinking about adding gunslinger right away. I really like that class, even if I disagree with the attending rules for firearms.
The Auld Grump, who freely admits that he has not yet looked at either the Samurai or the Ninja.... He likes guns.

But taking a quick glance at Samurai... weren't the Samurai primarily horse archers?
*EDIT* The most serious self inflicted injury that I have ever had with an archaic firearm was tearing the webbing of my left thumb with a flintlock. Ye gods, that hurt, not life threatening, but damn....
*EDIT 2* Looking at the webbing, I still have the scar, some thirty years later.