Something I think this game could use is a "screenshot" function, so we don't have to go through the PrintScreen process to share pictures of epic battles. Maybe just press a key or click a button in the corner (if you're trying to keep a mouse-only interface)
Another thing that I don't really have a suggestion for fixing, but know is a problem, is that there seems to be only one winning strategy; spread quickly and destroy what's left.
Once a player figures that out, the game pretty much becomes a grind. They know what to do, how to do it, and they can do it easily, then they win. Would it be possible to, maybe, give the AI players random "strategy" attributes?
Perhaps give each team a preference for which attribute they value the most, so they'll show preference for asteroids with that attribute, and make some teams follow a "spread and destroy" tactic while some set up a stalwart spot in the belt and slowly expand, and some amass fighting forces filled with fast, weak seedlings, while others' armies consist of slow, brutishly strong seedlings, while others' might have average seedlings that can take tons of damage. But you would have to make sure that the two strategies (or more) don't easily overcome any of the others, like it is now. A good way this might be done would be to allow seedlings to attack mid-flight. Expanding on the suggestions for patrols, you might be able to incorporate it into the Spheres of Influence; mark one asteroid as a "patrol asteroid" and have a certain percentage of its inhabitants go around to each asteroid in its range, then if a large group of enemy seedlings enters any of the patrolled asteroids' ranges, the patrol would either take the whole of itself and follow the intruders or just send a percentage of itself to follow them and attack them. Of course, it might also be useful to not have seedlings chasing down enemies, if the enemies just stay in place to fight off the attack, and you don't have a huge group patrolling, but a line of smaller groups, it would form a sort of reaction; small infringements on the patrol would only take a few seedlings to take down, and the few seedlings would be able to do it before a huge back-up was caused, while large infringements would cause huge back-ups and the patrol line would naturally form into a large attack force.
A good feature for potential patrols might also be the ability to set up stationary patrols; just groups of seedlings that hang around in space and attack enemies that come near.
Alright, so now let's hope someone high up can make use of my rambley post...