Re: what is the most effective way to play as a smaller faction?
No, the Papal States are basically a "new" playable faction. They really need more work. This is just a "beta" playable faction if you get my point. Playing as them gives you too many advantages compare to the other factions: no Catholic faction will attack you, no family tree (once he Pope dies, you get a new one elected each time), etc...
Another way to play small factions is to become the vassal of a strong one. For instance in your case, at the beginning, if you can become the vassal of HRE, your southern border is safe and you can develop quietly until you're enough strong to be independant.
In a general view, you can not blietzkrig in SSHIP. You need to take your time to develop and to think where to expand. You have to build your economy to improve your armies and then you can expand but not too fast. Over wise, the situation can easily become out of control.
Under the patronage of Flinn, proud patron of Jadli, from the Heresy Vault of the Imperial House of Hader