Thanks for the welcome. I have tried what you have suggested. I made a pretty good attempt last night, but in the end I could muster enough to cinch victory. What seemed strange to me, though, was that although I had managed to colonize several asteroids, only one produced a flower. Therefore, at any given time, I had a single laser mine. The other seedling colonies had multiple. I'm surprised I managed as long as I did!
At this point, I think if I could get more asteroids to produce flowers so that I could have more than one laser mine at a time, I'd have a reasonable chance. Also, I think, for now I prefer the slower pace of the game. If there are any tips on how to encourage flower growth, that would be appreciated. Just has a note, i had colonized asteroids with reasonably high core energy - at least the core energy was higher than that of "enemy" seedling colonies.