Fundamentally though, the crusaders need to build a power base, or connect themselves to a power base. Which means they need to rule Egypt, and strengthen the Copts into a power base, or attach themselves to the ERE. Their homelands proved in OTL that they weren't the most reliable backers, source of strength, or overlords.
Basically, this.
The Crusades sent armies to the Holy Land, conquered territory, and then most went back to Europe. How do you get enough men to stay? How do you get them to keep a strong enough power base to defend themselves? And, of course, how do you keep the area 'Christian' when the population is largely Muslim?
Swearing fealty to the ERE would have been politically unpalatable (possibly impossible), but it might be one of the few ways to get the 'Holy Land' to stay Christian. IOTL, the various crusaders set up dozens of squabbling statelets (which, given the nature of Europe at the time is probably hard to avoid), which made 'divide and conquer' a lot easier when the Muslims attacked.
Having everyone under the aegis of Constantinople, and having coordinated defence, and 'nearby' reserves and logistics support MIGHT have enabled the Frank ruled areas to survive.
Actually, it's totally doable.
Just don't have Alexios I think the Crusaders in the 1st Crusade failed. Then he won't turn back and the Crusaders won't think they were abandoned.
I mean, the Crusaders were effectively glorified mercenaries working for Emperor Alexios I Komenos and any land they conquered was meant to be governed indirectly from Constantinople. They only reason why they broke off from the Empire was because they thought Alexios abandoned them.
Boom. Any consequent crusade, 2nd, 3rd, 4th, etc, would be under the aegis of a Latin-Greek coalition.