This is... wow this is incredibly impressive! Any feedback I have is nitpicky at best. But I can offer some ideas.
I think your ship here could benefit from some kind of acceleration curve. For instance, have you ever played Raptor: Call of the Shadows? That game, to this day, has a very unique control scheme for shmups where the acceleration of the plane is tied to the mouse position, but not directly. Rather, it accelerates toward the mouse, and the further away the mouse is, the faster it goes. Think along those lines.
I love love love the idea of starting the game over if you upgrade the ship. But if you're going to do that, those upgrades should be VERY significant. No 5% this, 1% that. Nah, we're talking 20%, 50%, hell, 100%. The game should become an entirely different experience if you upgrade. Just yeah also make sure you can't upgrade again until you defeat the next boss down the line, which I'm pretty sure you've already done!
Also a few more pickups along the way would be great. Different weapons like missiles and machineguns or auto-aiming lasers. Screen clearing nukes. That kind of thing.
Oh and one small trick for smooth-scrolling, non-repeating backgrounds: flip every other background image vertically. That way they'll mirror as they go but they won't get awkwardly cut off.
But I really do love what you have here! Congratulations on a great first game and an excellent choice of engine. :)