There was a lot of prejudice against the Byzantine Empire in contemporary medieval western texts. But I think that most of these prejudices are not justified. (For example: After the failure of the Second Crusade was it common in medieval western historiography to accuse the Byzantine Empire of treachery even when the crusader did some serious mistakes.)
1. No. It is possible to bring in some western/catholic settlers, but the conquered area is densely populated. It is beyond the logistic capabilities of the empire to plan an organized mass migration and expulsions of Greek inhabitants. Also such a policy would result almost certainly in failure. If the empire starts something like this, revolts would likely occur. Nicea or Epirus could use such a revolt to regain control over their territory.
Like in the other crusader states (or in most of the cases of larger conquests in the Middle Ages), the conquerors where mostly only a small elite which gained power over a large conquered majority.
5. But still the Catholics are a small minority. Therefore, some compromises are necessary. For the long term symbiosis and fusion of Western/Latin and Byzantine traditions seems to be the most promising way to ensure a stable government in the long term. The contested election of an Venetian (
https://en.wikipedia.org/wiki/Thomas_Morosini) as the new patriarch of Constantinople was not a good way to raise the acceptance of the new regime. In 1214 the pope Innocent ordered his legate Cardinal Pelagius to enforce the remaining Greek clerics to accept the Latin rite, and tried to impose so a church unification by force. Pelagius was confronted with strong resistance and failed because emperor Peter allowed the Greeks to reopen their churches.
2. In general too much power for the Venetians and for the nobility. According to the Partitio terrarum imperii Romaniae, it was planned, that the Emperor should only control one quarter of the former byzantine territory. (to Venice three eights, and the rest to other crusaders) (
https://en.wikipedia.org/wiki/Partitio_terrarum_imperii_Romaniae). If you want to strengthen the trade of the Latin Empire, you had to strengthen native merchants, which could anger the Venetians.
To reform the Latin empire, you have not much time. Your POD should be between 1204 and 1224 (Fall of Thessaloniki to Epirus), because really soon the Latin empire lost most of their territories except the Area around Constantinople and the de facto independent states in southern Greece.
My suggestions are:
1. Allow the orthodox clergy to elect a patriarch, which needs the approval of the Emperor and the Pope. Also allow their liturgy, but start some form of dialogue to create possibilities for a church unification in the future.
2. Reduce the influence of the Venetians without loosing their support. Therefore still allow them to trade and have some influence in the Empire, but don't allow them to influence or decide the really important decisions.
3. Don't destroy parts of the Byzantine Bureaucracy, use them to support the Emperor (
https://en.wikipedia.org/wiki/Latin_Empire#Organization_and_society + also economy and society on this article)
You also need to gain more financial resources. The Latin Empire lacked them, because the Emperor controlled only small parts of the Empire, the Venetians controlled the trade, and where opposed towards tolls, and Constantinople was devastated by the fourth crusade. Selling relics to western Europe would improve your financial situation but contradict goal 1. and damage your prestige.
4. Try to support the other crusader princes in the area, especially stop the Komnenodoukas dynasty from Epirus. (
https://en.wikipedia.org/wiki/Empire_of_Thessalonica), and gain the upper hand over the princes.
5. Try to avoid any war with Nicea. You don't have the resources to wage war against them, even if you win, further conflicts with the Seljukes of Rum or with Trapezunt could occur.
6. Some of the problems are so severe, that it is impossible to fix them in short time. There are also reasons, why the political system of the Latin Empire formed in this problematic way after the fourth crusade. Also the authority of the Latin Emperor seems to be limited. Therefore are radical reforms really difficult.
7. Luck and incompetent neighbors.