I figured out a great strategy for hard-to beat infection levels. Buy the beam upgrades, unlock the Miner and at the beginning of the round, don't spend your money on Reactors but just build as many Miners as you have cash for. I promise it will pay off, and it's the only way I got past all the Infection levels. Also, stay away from big ships on those particular levels unless they are the ones that launch fleets of little dudes.
I think this game is silly because there are too many possible ways to organize some of the puzzles. You just have to keep trying all the permutations until you get it right.