Personally I think we are starting to suffer from getting far to specific about certain things. ie, grasshoppers and giant wasps, the anatomical parts of the mavens and contact with the avians. The pay off has been rather low, and for a 'restart the human race and explore the solar system' mission its pretty specific. Im not saying they shouldnt be worked on, but maybe go for something more ...broad I guess? Like research into decreasing cybernetic rejection in the mavens? Or into the addition of cybernetic weapons into their body? Its just my opinion, but it currently has been more research for the sake of research rather than a direct purpose that can be useful. Meh, just what I think.
As for where we are now, I think ignore the robot for now, or at least this next turn. Reason being, we havent actual checked any of the other facilities when we should. Is there a robot in everyone? maybe there's a facility where one is already broken down. While we could go the glue route, it was stated that the door wont open, which means we have to cut it open (probably through welding), and that in itself may turn out badly. The robot seems to be programmed to stay inside the facility and keep the door shut, so if we break the door... might not end well if it goes a little nuts. Also there could be alot more that just the one robot which would be futile.
Also, I think we should pull our guys back from meeting the moonies. We are currently sending them into the aliens territory where we will have no contact or know whats going on. So they can pretty much study our entire race, our weakness's and genetic code while we will still know nothing about them. Neutral location needed.
Finally, how about a space-port/ship yard so we can add a few more ships to the fleet. Our current ship is on the out, and it could also serve as a center of commerce, government and military power between the colonies.