Well, I'm playing this challenge. MY 2287 and it's a won game. Four Booger factions eradicated. I have as many bases as the other two combined, 35-40. it will take some time to gas all the Progenitors to death, but the issue is no longer in doubt.
Biggest problem with this approach is that all the other factionns are the same color. Use all the same base names and their names are differentiated only by 2-2-... after both H'minee and Caretakers. On more than one occasion, I attacked a faction with which I was at Truce, because I couldn't distinguish which faction's units were there.
No reason not to elect yourself Governor on the first turn, adds one energy to each base.
H'minee hates GREEN as much as Free Market. I've been GREEN almost the whole game, since about 2145, when I discovered Empathy.
Planet rating doesn't help on defense, so worms were the best relative unit to the defensive capabilities of the Caretakers. (Base 3:2, +20% for Planet rating of attacker, +25% for Caretaker Defense, +25% for Resonance armor --- 3.6:3 if life cycle of native unit matches Morale of defender. Compare to 4:3.75 for impact attacking Res. Armor. Moreover, frequently the attack can be made in fungus (even rocky fungus) which makes 5.1 or 5.4 to 3 vs. 4 to 5.5 or so.)
Basically, I used worms to keep the bordering Caretaker factions at a distance until I developed Doc:Air, then commenced to roll them over with X Missile Needlejets.
I built the Command, the Cyborg, the Maritime, the Cloudbase and, of course, the Neural Amplifier. Took the Genome and the Empath. Still lack the CDF, the Weather, the Merchant and the Virtual World.
Ought to be done by about 2350.