My two eurocents:
A) keep the system as simple as possible, for gameplay reasons;
B) found the difficulty of building large empires not on socio-economic indicators but on the abstract, fundamental root of the problem: organisational overcomplexity.
The reason for B) is twofold: first of all, it couples well with A). Secondly, it helps identify intuitively (in the game) the problem and look for solutions.
There should be a complexity score and a organisational capability score for each planet, system, sector and for the entire empire. If the former is greater than the second, efficiency drops proportionally and at a certain point a progressive rebellion chance kicks in.
So organisational complexity could be increased on all scales (imperial, sector, system, planetary) by:
1) size (number of planets at the large scales, population at the planetary scale);
2) different races (with a quadratic weighting formula, so that two roughly equivalent subgroups are more likely to cause trouble than a small minority to a majority)
3) different unsatisfied needs. The needs should be very few and intuitive, like:
- economic development;
- social develompent: arts, entertainment, politics, rule of law...
The need should be relative, of course, to a termin of paragon. This could be the average of the empire plus the neighbouring systems, regardless of who owns them.
The idea is that, if parts of an empire, sector or system have different needs, then the organisational complexity of the aggregate will increase. maybe we could use again a quadratic formula to penalise more split-in-half aggregations. The more unsatisfied needs a planet has, the more complex it is to manage.
Countermeasures come with technological or sociological development, in the 3 possible direction:
1) enanced organisational capability;
2) homogenisation, harmonisation of the races (enlightened or violent...);
3) solving the immediate needs
To satisfy the economic development need, one could lower taxes or invest in economic infrastructure. To satisfy the security, have more ships around. To satisfy social development, tweak social engineering, build the necessary socio-political infrastructure.
Events can change these scores at any level. For instance, my idea of transcendence through assumption of templates (proposed in another thread in braistorming) would couple well with this: after the acquisition of a template, complexity hikes up a bit, for good - unless a rebellious part secedes and refuses the template. Random events, piracy, enemy blockades or internal political instability, as well as economic crisis, would fit easily too.