From what I have read here, I think the problem is that they are misunderstood.
The synthetic style has significantly different strenghts and weaknesses then the bio styles have among themselves. If you are trying to do a colony rush you are emphasizing their weakness, which is the early games limited production. You can't go without grabbing a few colonies to slow down your bio neighbors and preparing for a high pop cap in the early midgame when you are shuttling your population.
Your main focus however should not be grabbing as many colonies as possible, but to build up critical infrastructure at your home planet to start playing to your strengths, which is rapid population via assys and high population caps. Effectively this means blasting your ealry money on asteroid mines or -if possible- an early durantium refinery instead of many colony ships. This is the more important part to solving the raw production problem, then the changing the home system. Changing the home system to kryseth maximizes one of their strengths (pop cap for small worlds and high growth rates with high manufacturing),
You will probably end up behind in colonies. The synthetics have the least issues with this. A bio race needs 10+ (assuming one contributing planet) turns to replace the pop for a 6 pop transport module, the synthetics need 1 turn. Invasions are a strength of synthetics.
The Iconis star system doesn't emphasize their strengths enough with only one habitable planet and one asteroid group. Better systems are basicly any system with 2 asteroid groups and more then one world: Iridia, Iconia, Kryseth, Arcea and Torus. The Torus system in particular together with the aquatic trait might be very interesting, too since the aquatic worlds give a 25% production bonus (-> stacks nicely with early asteroid mines!).
For me it is too early to definitly say whether they are underpowered. MAybe they need a little something which helps them out at the start, but they probably don't need a lot to be competitive again. Giving their tech tree capitals and the Iconis system 2-3 asteroid groups (one in the habitable zone for early access?) might actually do the trick.
For the AI however I am not so sure this will be enough. They might need their own AIDefs to use this to its full extent.
Addendum: One more thing you can do for your early production: get the free colony ship from benevolent = +3 free population followed by another world so you will have 4-5 (depending on homesystem) worlds in any scenario (Not sure if the constructor trick might be better though).