I don't know how true this is, but my impression is that Constance's marriage to Henry VI was also met with huge outrage and disbelief among William's lords and other subjects - yet William still managed to push it through. Going by that assumption, a marriage to one of Andronikos' sons doesn't seem too hard. The result likely wouldn't be a Greek king of Sicily; but Tancred lazing around on his throne with little to no serious threats. The Pope's possible protests could be an obstacle, but they might be prevented by letting him know "it's either this or the Hohenstaufens".
In Byzantium, Andronikos having an (explicit or implicit) marriage alliance with Sicily could have some interesting consequences - the throne might stay in the hands of one of his sons even if he has to go. Byzantium may be in slightly better shape, and help the Crusaders (or rather: help Sicily out in its activities after the fall of Jerusalem, and let the German army pass without serious difficulties).
As an aside from that scenario, a military action in Cyprus may be worth considering - not to prop up the separatist Isaac Komnenos, but to seize the island.
In Byzantium, Andronikos having an (explicit or implicit) marriage alliance with Sicily could have some interesting consequences - the throne might stay in the hands of one of his sons even if he has to go. Byzantium may be in slightly better shape, and help the Crusaders (or rather: help Sicily out in its activities after the fall of Jerusalem, and let the German army pass without serious difficulties).
As an aside from that scenario, a military action in Cyprus may be worth considering - not to prop up the separatist Isaac Komnenos, but to seize the island.