I think you are doing fine with what you describe. For me it depends on the enemy civ I am facing. If it's the Habsburgs you can destroy them with only spies and mafiosos. It would be hard for a good player to lose the Habsburgs using the Italians. The same almost goes for the native and african civs, they have one explorer who usually will run into your units. When he does, I trap him by building mines around him. Whenever he decides to wake up he steps on a mine, dies and remains useless. While he is down, you can march right into an enemy colony with Spies and Camorisitas and finish the game. Against alot of other civs, I can use large groups of Alpinos, Bersagliere with alot of buildings around them and for the most part they will withstand any enemy invasion. Artillery works great against enemy infantry as well. All the Italian units counter well, so if I am getting hit by a lot of cavalry, I will use Halbreiders and Dragoons to stop the attack and it does work for the most part. Italian infantry is weak in hit points and attack but redshirts have good attack and elmeti have alot of hp. I always use redshirts, elmeti sometimes but they cost 4 pop. I usally will include at least 5 but sometimes many more priests, I have used as many as 25 to try to boost the attack of the units. Your military can win vs most of the civs on here, you just need loads of them, recruit units and send them in shipments, but get alot of them and you will be fine. Whenever you are facing a civ that obviously has stronger military units than you, you have to use Camarisitas. The Americans and the Dutch are probably the hardest civs for the Italians on here because their units are strong and they have a million fur traders, envoys and explorer dogs. I try to send spies to the back of their colony and burn their buildings, it does deter them from attacking you giving you a chance to get strong early. It took time to be able to win against them but I have it down most of the time. Use your statues in front of your colony early against any European and Anglo civ because they will try to place forts and military buildings close to you. Walls also help too, some people think using walls or petards isn't fair but why have them available if you can't use them.
I am too old for games like this but too young to resist playing them