I have just finished reading a very interesting book called "City of Fortune: How Venice Won and Lost a Naval Empire" by Roger Crowley. My background reading on the Crusades had already alerted to me to the influence of the Venetians in the 13th century, but I had not appreciated the full range of their impact. In true wargamer fashion the 'butterfly' effect began to kick in, "wouldn't a small Venetian army be useful?, so many potential opponents, opportunities for land and naval actions." The same sort of thing occurred a few years ago when I read John Julius Norwich's trilogy on Byzantium. Before I knew it, I had the first (and up to press only) installment of my thematic Byzantine army raring to take on Bulgars, Khazars or any of the quite extensive list of potential opponents. (Even themselves if there was a coup!). However, as you guessed, the butterfly only lingered for a short time before winging its way to another project.
So far I have managed to avoid plunging into building a Renaissance Venetian force, though I was sorely tempted by the sight of some galleys at the Triples show.... That being said the Venetians could be set against Tartars, Ottomans, Pisans, Genoese, Hungarians or Norman settlers. They could fight between themselves for control of disputed islands. There could be small scale galley actions involving attacks on convoys- no need for dozens of models to refight Lepanto! The most interesting part was the chapter on the siege of Venice in 1380 . Genoa, aided by other Italian states and the Hungarians almost succeeded in defeating Venice. There is plenty of potential for small scale raids on fortifications, actions between rival bands of condottieri and attempts to sink ships in channels to block supply routes.
If you have started to look around for a book to read whilst sunning yourself on holiday this summer Crowley's book may be worth a try. His style can be a bit of an acquired taste, but if you can get beyond that there may be enough material to furnish several scenarios for those winter games nights. The Junior General website can provide printable galleys and rules to dabble in the period if you do not want to inflict further damage on your wallet.