- The ~33,000 crusaders the French contracted the Venetians to transport could have actually showed up.
These estimation were wishful thinking : giving the Anglo-French war, German-Pontifical conflicts, general disinterest for the crusades, etc. All of that would be huge obstacles.
- The French could have had better estimates, and only contracted for the ~12,000 that showed up.
The problem wasn't only the guesstimate made by Crusaders , than the number of sailors and ships it required (when the doge tried to lower the price to the actual ammount, they still didn't have enough). Crusaders had none of them (for quite good reasons), and Venice was to supply it, including ships (meaning a net commercial and demographical risk).
Crusader still lacking money (the whole expedition was half-assed), they had to comply before Venice demands.
- Alexios IV could have presented the Crusaders with a more realistic proposal
There would be the huge problem of excommunication after Zara, and half of the army turning back to Europe. Lacking any kind of religious legitimacy (Byzantines lacking concept of Crusade to begin with, even if we wanted to try that).
Furthermore, I'm not sure more realistic demands could have been easily reached : you had other than money, as in accepting pontifical supremacy, giving troops to Crusaders, basically a pro-Latin policy that would have make him expelled at best.
Remember that it's a much modest pro-Latin policy that ended Commenos dynasty and put Angelos in charge.
Assuming that less than 8,000 , excommunicated (I grant you the excommunication was rescinded, but going further in error wouldn't help), hugely divided (IOTL they figured out a leader afterwards), and not having a clue on how to reach Egypt without being hijacked regularly manage to reach Alexandria...It's not going to end well, for them.
(And of course, their allies in Syria knew a political division the very next year)
The whole expedition was probably one of the best medieval equivalent, in matter of feasability, of Sealion.
The point is that we simply assume that the Crusade got to Egypt in enough numbers to matter, and then those Crusaders went on to win.
Well, I tried to answer that in my post : from what we know of their plan, they didn't wanted to conquer Egypt itself, or even trade it against Jerusalem, but advancing in a more fertile and less mountainous road than Turkey up to Palestine and make junction with the Kingdom of Jerusalem.
There, they would probably have formed their own fiefs, more or less dependent from Jerusalem (IMHO, probably less than more), and probably in the hinterland. I doubt they would go to hinterland of Tripoli and Antioch (Bohémond IV antagonized everyone in the region) immediatly, but that's a distinct possibility for later : maybe taking one or both of his titles, claiming to be vassals of the king (maybe for Leo I of Armenia in Antioch), with a good enough reason, as Bohémond ruled out the Latin patriarch of Antioch and called back the Melkite Patriarch.
I could see however, Venetians pressing for more influence in Cyprus and Jerusalem against Templars and Genoese, and Fourth Crusaders could have been pushed to attack Isabelle if needed and replace her with some one else. In this case, they'd antagonize everyone in the region, especially Ibelins : a counter-alliance with Muslims against Fourth Crusaders wouldn't be to be ruled out in this case.
If they don't : they would rule on rather ingrate lands, and more prone to be attacked. Ascalon and Gallilée would be prime lands, that said.
So, maybe something like this.