Very simply, what if instead of petitioning the Pope for aid, the Emperor of Byzantium instead sends out priests and recruiters across Europe. The Komnenids were wealthier than most Empires, and hiring and drilling a fresh army of Franks and Germans to back the Byzantine forces seems as valid as any other plan. Plus, the Emperor has total control, rather than concerns as to Crusader loyalty.
Could he recruit (and afford) enough Frank and German peasants to make into a Latin Legion, and could they conquer and settle areas of Anatolia to this day?