I think the longer the Hohenstaufen are functioning in Germany, the longer the Interregnum. Given the policies of Frederick II in Germany, during his reign, it would be extremely difficult for his successors to achieve more than a ceremonial control of Germany, as a best case scenario. Perhaps enough to retain the prestige of a HRE emperor, but probably irretrievably difficult to regain lost ground -- realistically, only Swabia and a few other regions of Germany remain as real Hohenstaufen fiefs. The best thing for a Conradin or theoretical surviving house Hohenstaufen in Germany is to recognize this.
Frederick was going for the riches and sophistication, latitude of action, and power of the South, with its fairly continual history under Hauteville and Hohenstaufen rule of the legitimacy and effectiveness of centralized government. And Frederick was a cultural Sicilian far more than he was German. He hardly spent any time in Germany, at all.
Frederick's immediate successor, Conrad, and then Manfred, both realized these realities. Germany was no more than a resource for them.
Absolutely, the Papacy had a tremendous soft (and temporal ) power in the service, as I previously indicated, of a couple of pretty competent Popes. The Hohenstaufen were not the only rulers of Europe who had their differences with the Pope at that time, though. Effective diplomacy might blunt the Pope's power. Again, if the anti-Hohenstaufen power-base in Italy is chastened enough to disunite them, a powerful ally to any Rome-sanctioned external invasions by an ambitious prince are going to be much less effective. Charles being crushed would be a powerful deterrent to such princes. I'm doubtful of an effective "crusade" being called by a Pope. Too many polities were already ignoring such calls and the Hohenstaufen were no Cathars. Apart from the Italian Guelph, I don't see the emotional resonance for such action.