No, avoid writing at all costs. People hate reading. You would have to come up with something graphical. So clear a wave and the ship flies to the middle of the screen and comes to a stop at a base perhaps or some sort of way station like it is parking. Would at least explain why it has access to the 'shop'. It it was changed to the Hanger Bay, where you can buy upgrades and buy repairs etc rather than auto health regeneration. You could add smoke coming off the ship to indicate damage. Then when the next level starts you fly away from the waystation again.
As for the auto shooting I think it could work. Maybe only on appropriate ammo, so the darts in the shop could clearly indicate this is not auto fire. Adding a differential to some of the ammo types.
Of course you don't want to change your game too much, I get that, but you do need something to tie the different parts together a bit more. At the moment after a level it says "Back to menu" like the game is over. If it said "Landing in Hanger" that would be better would it not?
Anyway, look forward to seeing your improvements. I thought the cards could do with being a bit more colourful with bigger images portraying the upgrades a bit better. So again I don't have to read anything! You would be amazed at how people never read anything unless they are really committed to the story. Like skipping cut scenes and dialogues.