Anyway I don't think DA in particular need a fix so much as the whole population growth system. I don't like the "planets are baby factories" system right now and I wish your population growth wasn't so proportional to the number of planets you own. Whatever solution fixes that would apply to DA balance too.
To get out of the current situation where population growth is proportional to number of planets and organic + robots always beats pure organic or pure robot growth, you'd probably have to do something like this:
1. Organic natural population growth is on some sort of curve where large populations can make more pops per year than small populations. (At the moment there's effectively a penalty for planets with <10 population, but we all know how easy that penalty is to circumvent in the mid-game.) Immigration is a separate factor that adds on top and isn't dependent on the existing population (but it obviously takes growth away from some other planet). This way, your population growth in the early to mid-game on comes mostly from your populous 'core' planets (spreading out through migration and resettlement), rather than just your raw number of colonized planets.
2. Machine population growth is basically proportional to the number of roboticists/replicators working on the planet. (Cloning vats could also be changed to give a job that adds flat organic pop growth, rather than just passively boosting natural growth.) In one of the pre-release versions, machine empires were allowed to invest heavily in robot factories, but the devs panicked when Kaiser Johan actually did this in the dev clash; in response, they locked the assembly plants to one per planet (plus gradual upgrades from improved administration buildings). I think this was a bad move: machine empires should be able to build lots of pop factories, it's just that any extra factories (i.e. not counting the jobs provided by the admin building) should be very expensive to run, so there's a real trade-off in short-term versus long-term power. Remove the per-planet limit, and then your ability to build robots isn't just proportional to how many planets you have, it's a question of how many resources overall you can invest in population growth.
3. Vanilla Machine Intelligence and Determined Exterminator should have access to some better robot growth options, to make up for their complete inability to grow organic pops. This extra bonus should *not* be available to Driven Assimilators or Rogue Servitors. (If RS are underpowered, I think the solution has to be to make their existing machine pops better through some kind of effect of biotrophies, rather than letting them ignore biotrophy population and focus on spamming machine pops.)
4. Synthetically ascended empires can have an optional 'synthetic supremacy' policy that increases robot growth and/or productivity at the cost of mandatory 'assimilation' living standards for any organic species they acquire. Alternatively, let them make 'synth worlds' that are uninhabitable for organics, but can house much larger synth populations than normal. Either way, true synth-ascended empires need something to be able to compete with the growth potential of regular organic empires (bearing in mind that these empires can get droids on top of their natural growth).