The trick to level 6 is that the enemy ships spawn in a fixed pattern. Put all of your upgrade points into fighters, then have them cycle between right in front of your frigates(at max range), the asteroid field, and the base (have them dock when moving back to the base).
The trick to the last level, since it's virtually unwinnable without it, is to immediately throw away everything but a few fighters, and build two cruisers ASAP. One defends your base (especially against beam frigates), and the other attacks the enemy base (you can ignore the enemies outside of your intended attack vector, they won't notice you). It takes a long time to kill the enemy base, but you should manage it. Keep some fighters on the defending cruiser, and some fighters at the base to deal with the enemy's cheap jump of bombers right behind it, which repeatedly spawns.
I still don't know why he didn't make the last map a nearly symmetric skirmish, given that there was an enemy base right across from me for the first time, and enemies had been jumping in for the first part of the game, but it was admittedly fun to have the cruisers I just unlocked wreck everything that came my way.
The skirmish was interesting. Tried it on Medium, and I'm not sure that the enemy wasn't getting double the credits, but I still overpowered them because they wait a long time to build a second mine, and tried to tech up after running out of resources, resulting in my fighter swarm killing their two anti-fighter frigates that they sent out one at a time. I'm not sure why their mining ships were labeled as '?' until I ordered my units to attack them, but it didn't help them.
After that, I tried skirmish on hard. The same strategy killed them. Five scouts, a second mine, take the center mine, then continue by massing fighters. The enemy sent a beam frigate after its first anti-fighter frigate, indicating that it doesn't really understand counters (might be following a set rotation). Appeared to use the last of its money on a mining ship.
Overall, a really fun game that pulls off the RTS theme really well without running into the difficulty of programming a pathing algorithm more complex than 'calculate vector and thrust'. My complaints would be the kind of janky movement (especially visible on the missile level), and the fact that the 'a' command seems to tell my units to attack the closest enemy, rather than the enemy closest to the mouse.
I am kind of surprised that the giant enemy ship from missions 1 and 5 doesn't reappear in the last mission, given all that foreshadowing, but the ending certainly justifies that.