However, I'm not 100% sure I'm scoring very effectively. The most I've had is nearly 14 million by stage 4, and the lowest score has 10 million by stage 2

All I know about the scoring system is slash at stuff, collect the medals, break parts off the bosses for more medals, don't break your medal chain (especially when you get max medals at 100k), and milk the destructible projectiles that come out of bosses (which I'm honestly not very good at). Is there anything else to the scoring system?
Since this game only gives you one extend, I assume you're not supposed to die a whole lot to reduce rank


Oh also, I didn't look at the tutorial that closely on the front page. What does pressing all three buttons do?
P.S. Where are you guys getting the ship names? I'm using the girl in the middle named Rosalitta, but I'm not seeing the names used in the high score thread at all.