Good work on this game!
If you're having trouble on lvl 4-16 - try the missile swarm (not the double - don't know why but it sucks even though it's more expensive). I was having some real trouble the first time I tried it with lvl3 beam. It took a couple of plays through 3-14 to get missile proficiency up to lvl 99. After that, 4-16 was a lot easier.
Oh, and the regenerating shield on the second ship type recharges ***only when you're not firing***. That would have been helpful to know earlier on. :o
Keep the awesome games coming!