I'm afraid getting all of these lands is too tall an order.
The most i can see them getting are the imperial borders after the nicaean restoration.
Anyway, i think the best PoD for this would be snuffing out Nicaea as a contender for "unifier of the empire". Since i made a thread about it, a defeat at the Battle of Antioch-on-Meander (1211) against the seljuks would be the best starting point we have, IMO. But the problem lies in that there would still be other powers wanting to conquer Constantinople from the latins -- the bulgars, the epirotes, the seljuks themselves and, lastly, Trebizond. For a small state so geographically unfavourable to conquer Constantinople in this scenario is improbable to me.
The Ottomans started later, with less, and did better - so I'm not going to agree on that point. However, this starts on the premise that Trebizond and Nicaea take each other out early. If Trebizond reacts to the situation and makes a Greco-Turkic Roman state, hopefully converting some Turks in the process, then they could exist as a long-term fragment of the Empire, pushing the Nicaean Empire back over time. Which Constantinople has the advantage of controlling the Black Sea, an Anatolian Trebizond has the advantage of being able to expand in the Middle East, whilst Nicaea has to fight a successful Trebizond, or Europeans with all the diplomatic difficulties that entails.
Hmm. you could have Timur pillage and burn most of Anatolia, but skip Trebizond for some reason. What's left of Turkish Sultanates would be of no threat to anyone for a long time. Trebizond could capitalise on power vacuum better than Nicea, absorb it after it too was weakened by Timur, and then conquer Constantinople from Latins.
Perhaps Trebizond see the writing on the wall and submit early, essentially pulling a Muscovy and becoming an enforcer for Timur? Nicaea and the Latins fight each other, whilst Trebizond takes control over Turkish Anatolia, Armenia and Georgia - sending mountains of tribute back to Timur with the hope it all collapses and they can stop paying? I dunno if Ghazis were a thing, or if they'd even co-operate, but if Trebizond didn't restrain them invading Nicaea, but instead took 10% of the loot, and 30% of the loot went to Timur, that could be a game-changer. The problem would be bringing them back under control....