Decent strategy but you should always take Rome ASAP. Especially if that is the only city the Papacy owns. Send your best full stack of men and your best general (not your faction leader) and take Rome. Make sure you bring a diplomat with you. I also recommend at least 2 good spies so you can attack on the first turn of sieging the city.
Do NOT kill any Papal armies outside of Rome itself, using the night attack feature if you must when you siege the city. Only kill armies in the city.
Once captured, immediately get peace, a full alliance with trade rights and military access both ways (you can't get trade rights or military access from them if they have no other cities). All of the large Papal armies outside of Rome will now protect you, and as long as you keep a diplomat by their armies, you can do whatever you want across all of Europe with the Pope backing you up.
Hope this helps.