I'm playing a Sicilian campaign right now (VI, hard, GA), using your advice: I just took Naples and after that, did nothing much except for massive economic, and, to this end, shipbuilding. After I had established a network of fleets in every sea, I just put every heir I got into Naples and that was that. I was making around 9000 florins in profit in the end (the end being my war with the French, more on that later). I also trained bishops, later cardinals, and sent them out to convert the world, and also to keep tabs on the potential opposition. Absolutely nobody wanted to go to war with me. The Byzantine auto-ceasefired, as we had no contact after I had taken Naples. I never realized how awesome Naples could be as a trading province, easily making 3000 fl per turn with a good governor. It was quite overshadowed by Sicily itself, though, which at one point (when no coastal rebel provinces remained) made more than 7300! Both figures with highest farming and trade building and an eight-feather-governor, of course...
With my family multiplying, my standing army soon consisted of around twelve to fourteen regiments of Royal Knights plus the mismatched spearmen you get in the beginning. These I sent on a daring foray into Constantinople, which was rebel, because the Emperor had just died of a disease with no heirs. Unfortunately, I had to withdraw them when I realized I could not hold the province with so few men. Other than this short-lived adventure, I just sat tight and made ridiculous amounts of money. Around 1280, I had a million. Owning just three provinces, I had a million! Nobody ever bothered to get into a war with me, no sinking of fleets, no nothing. I was too insignificant, and too hard to get to, the Pope sitting squat in the way of any potential invading armies. This is actually a huge advantage: You can expand by sea, if you want to, but by land, nobody can easily invade you. Twice, the Germans kicked out the Pope, their large armies sitting on my northern borders, ready to invade, but the Pope returned with large numbers and shoved them back again.
Having a million and slowly running out of building options, I decided to build an army like the world hadn't seen, then invade somewhere challenging. I was (barely) leading in GA points, just by sitting on my homeland provinces like a hen on its egg. The Germans were very powerful for a while, and actually outscored me, but they disintegrated under the onslaught of the most powerful France I have ever seen (when AI-controlled...). Spain had swallowed most everything that had once been Almohad territory, but the Egyptians firmly held them back. A while later, the French began invading Iberia, finally managing to secure all of it, destroying the Spanish in the process. Byzantium had been absurdly huge (reaching up to Moscow and Prussia), but as mentioned, stopped being a faction. Poland picked up the pieces and actually held Constantinople for a short while, before being mostly destroyed by rebels and the opportunistic Hungarians. The Golden Horde had meanwhile conquered everything east of Volhynia and north of Armenia (as they seem bound to do). The French sent several crusades and conquered everything up to Tripoli, where they were stopped by the Turks, the Egyptians and the returned Byzantines. They had wiped out the Germans and so had basically the western half of the map.
I had been building gold-armored Chivalric Knights in Malta, gold-armored Halberdiers in Sicily (plus church, monastery, reliquary, cathedral for their weak morale), and gold-armored Arbalesters in Naples. My plan was: Invade the French somewhere they have large armies, defeat and kill as many men as possible to lower loyalty, basically deliver a shock that sends them into civil war as quickly as possible. My chance came when the Spanish reemerged and fought for their ancient homelands in Iberia. For a few turns, they could establish themselves there, then the French sent in large armies and killed the heirless king in battle. Cordoba went rebel, as well as Portugal and Leon. I quickly moved in and secured Cordoba, while the French took the rest.
My main objective here was to get my unbeatably armies (four stacks all told) into direct contact to a lot of French territory with a lot of French soldiers in it, without winning a naval war of attrition first. Galleys simply can't stand up to Caravels, except in numbers, and I didn't have many more ships than I actually needed to keep a little trade going and my homeland protected.
Despite losing on the high seas at first, my armies made astounding progress in Iberia. The first turn of the war, I took Portugal, Granada and Morocco without a fight. Two turns later (after castle-storming), it was Leon and Castile, again without a fight. The French just kept withdrawing, even when they outnumbered my high-tech armies by two or three to one. The only casualties I had was in sieges, and as the French never just abandoned a province but left as many men as fit in the castle, these mostly lasted one turn, thus costing the French many more troops than me. This was necessary, though, as I couldn't reinforce by sea. It took a while to decimate the French navy, and I only made it with a lot of Byzantine help. Still, on land the pattern kept up: I invaded, French withdrew into castle. Two turns later, my slightly diminished armies would go onward, only to find the French retreating again. By now, my border provinces are Frisonia, Lotharingia, Burgundy, Milan, Provence; Wessex; Tunisia; and of course Naples. All this in less than twenty turns. Despite having almost no trade anymore (I was just barely able to keep open the route from Sicily to the Black Sea), my treasury is coming near 1.3 million fl, and I'm recruiting like crazy. The French even invaded Naples once, and suffered a very narrow defeat. But mostly, they just withdrew.
Lesson learned: Sitting tight is so easy with Sicily, it's laughable. And building a super-army is no fun at all: You don't get to see those guys in action, the enemy always withdraws.