I would think that you are far too optimistic about the future. Hungary will probably be Hungary,they will most likely act just like Hungary(no shit) did when they were in a union with the Austrians. The Hungarian nobility will most likely stir up trouble. There is also the matter of religion. Either the Greeks or the Hungarians will stir up trouble if their side of the religion is not favoured,and a union of churches would be very difficult. There will be a lengthy period of instability in the empire.It's really a great tl.. If u look at what this woul bring to the reconquest of Anatolia plus you gain,
1 Hungarian mounted archers and hc .. The balance of additional force would go hard in the byz favor
2 a stable gov , as long as bela lives,
3 Serbs under control
4 manuel left a very large fleet so if this is maintained Venice and the itialian cities could be kept at bay
5 per treadgood byz in 1200 was at a peak of its wealth with a unstable gov, here u have the wealth plus stability.
6 after Anatolia reconquest do u regain a weakening southern state in italy , also putting pressure on the pope
7 or propping up and formalizing the crusader state dependence ?
Anyway reestablish the Anatolian border in the Taurus mrns. And you would see a cascadeing wealth. The western Anatolian areas would not have raiders, the central areas would have livestock, and the final borders would have hardened warriors. The increased forces, wealth, and navy would give the byz great opportunities for the future. Now figure out a way to raise the sea walls, thicken the walls ( to hold off cannons in the future), keep up the fleet ( keep trade going) and you are powerful.