Second basil because that's a strong Byzantium that can credibly claim the status of empire without simply being the pan Mediterranean Roman empire.
There’s also the Komnenoi to factor. They took over most of the Northern half of Roman Anatolia virtually unopposed with their invasion of Trebizond starting before the Fourth Crusade happened. They had the support and backing of Queen Tamar the Great of Georgia as well.Alexios Angelos would likely retake the throne c. 1205 and would likely get overthrown by the Laskarids or the Palaiologos.
I think that given how the Komnenoi were already on the move at the time of the sack that they’d be the most likely to succeed. The Laskarids can’t be discounted but the Komnenoi having better claims and momentum should give them the ability to take back the empire.There’s also the Komnenoi to factor. They took over most of the Northern half of Roman Anatolia virtually unopposed with their invasion of Trebizond starting before the Fourth Crusade happened. They had the support and backing of Queen Tamar the Great of Georgia as well.
Theodore or even Constantine Laskaris would have to deal with the Komnenoi who have an even better claim to Purple than them. Both Alexios and David were quite militarily competent as well, so I don’t see the fight being in the Laskarids’ favor.