Though more to the point of the thread, The Palaiologos might have fostered a Renaissance of sorts if they managed to stay stable, and the best way I've seen for that to happen would be a stronger focus on retaining their land in Anatolia and hopefully expanding upon it. It was this land that was the most economically active for the Empire for all of its history outside of Constantinople itself. Not to mention it would give the Empire the manpower it needs to not need to rely so much on mercenaries, which was one of the reasons they did so poorly in the first place.
Of course they also have the issue of the Dynatoi to deal with. They would need a series of capable rulers all willing to act in the vein of Basil and the Macedonian Dynasty, all while remaining strong enough to deal with any internal rebellion without trouble. Given their history, this is probably the tallest order of all. Civil war was practically a Roman tradition after all.