As BG said, it's very difficult.
The plunder of Constantinopolis is unbutterflying, but maybe you could just avoid the worst parts as the murdering of Orthodox clergy. Maybe by convincing Monfort to stay in the crusade as he was not really enjoying the fact to attack the city. It would really help to have the urban greek clergy more encline to work with the crusaders after a time.
On the other hand, i don't see how to make the same with the powerful cloistred clergy.
A latin victory, or even a stalemate at Adrianople is compulsatory. Maybe you could butterflmy away even the bulgarian help to thrakian lords but i don't see how.
The Latin emperors couldn't avoid the extreme feudalisation of byzantine lands, but maybe can limit its effects in the proper "imperial lands" of Thrakia and Marmara sea coastlands. Maybe by making a sort of agreement with greek lords as FIIB said, he could even take the north part of the anatolian greek empire, forcing it to relocate itself in Philadelphia.
It would obviously make him more a Latin-Byzantine empire than a 100% Latin Empire.
But I think that you need, for keeping greek and turkish states out of Egean Sea and a fortiori out of Europe, a bigger support from italian states, both military and economically.
Of course, these same strates were more encline to exploit the Latin Empire's economy, rather to support the existance of a strong state, a fortiori if it's not a puppet state or obviously a state that claim to have byzantine roots.
For that, maybe you need some of Charles d'Anjou-like figure that manage to have both Naples, Sicile and probably Albania; and to hold it. If you manage to have this and to make, not an alliance, but a communauty of interest against northern italian cities and peninsular greek states, it could work.
Of course, after some times, this southern italian kingdom would likely have lands in Greece and would likely have friction and claims on Latin Empire lands. It could push the italian to ally themselves with anatolian greeks or if it's not longer, turkish states.
For a up-to-nowadays Latin Empire, i really don't see how. It could survive more longer than OTL, or even longer than post-1261 Byzantine Empire as a balkanic-state. But it would beyond difficulty to keep it existing up to 2011.