Didn't the Palaiologi already rule for more than eight generations? They seem to have established a pretty solid dynasty right there, maybe a serious Ottoman screw could guarantee an even longer span of rule as the Palaiologi didn't really show much signs of unpopularity or shaky legitimacy in our timeline (well aside from a civil war or two, which they won). Granted said Ottoman screw would need to allow Constantinople to survive for as long as possible while avoiding any kind of Roman wank. As one of the major reasons the Palaiologi lasted so long was due to the drastically reduced population of the Empire.