It can be done much quicker with Castille too, I have made number of suboptimal things which I haven't recognized until later. Perhaps something like 1408 is doable reliably. With some luck, perhaps 1405.
I am not sure about other plans. How can you get a core on Rome (even assuming that you got lucky enough to get other cores)? The only thing I can think of is PU and inherit everybody while annexing Papal States and selling Rome to one of the monarchies. But this plan has pretty low chance of succeeding within first 10 years.