So how about, they make a less gross overestimate of the people who show up?
Which rises an interesting question : who the hell was in charge of the estimation?
More seriously, while they barely accounted for 2,000 men at this point in Venice, the 6 envoyees still accounted for almost 17x more men. One can think that the mesestimation, while being hugely idiotic in terms of consequences, wasn't just due to miscounting (Venice wasn't going to work
gratis et amore Dei).
Don't forget that most of these Crusaders were French, from the North-East of the kingdom especially : it was eventually about, IMO, prooving that the barons could re-edit the epic of the First Crusade and that they didn't needed the king and more importantly the emperor* (see the
Crusade of Henry VI) to do so.
While there's a certain bombastic statement at work there, I don't think it's just random, and reflecting both desires and the network of a nobility, once conflicted with the harsh political situation (the tensed, if not outright war, situation between England, France, and the Empire).
*It can be pointed that once Constantinople taken, the crusaders dismissed Boniface of Montferrato as their leader, while he had an important role so far, in favour of the count of Flanders which was one of "them" and not vassal of the Emperor.
(Admittedly, Boniface was somehow suspected of hellenophilia as well, due to its links with Byzantium)
OTL, they contracted to transport 33 500 men, at 2 marks per head, and 4500 horses, at 4 marks per head. Total 85 000 marks.
You forgot supplies, squires and other personal. Which ammounted to 94 000.
In the event, just 11 000 men showed up. And with a great effort, scraped together 51 000 marks (originally, they managed to gather little more than 30 000 marks, IRRC, until they were reduced to go trough major cessions, see below).
So, suppose they contract for, say, 17 000 men and 3000 horses?
At the same prices, they wind up with 46 000 marks.
Which would still let them indebted : as you said, with great efforts, they scrapped together 51 000 marks.
Which doesn't mean they had this large sum on them, just like pocket money, but by futher usurery, with precious stuff or even lands being engaged or sold.
Even that was eventually completed by the 34 000 remise accorded by the doge to pay for the full armada.
Remember that Crusaders already had to borrow the initial money (for giving deposits) in 1203, when they first came to Venice, to have an idea of the financial problem.
Without counting supplies (which is absurd, but just for the fun) and everything that is not strict transportation...always makes a 11 000 marks difference at best.
You could technically have an even less important guesstimate, but at this point it would be admitting that the expedition was going to be a total failure.
What will they accomplish?
Minor nuisance Crusade?
With all the poor logistics, leadership disunity and all on they showed off...
I'm not saying Ayyubids would be in for a good laugh, but I don't think Crusader would have been able to go for Jerusalem : while not strictly impossible, doesn't look good, isn't?