I thought the game graphics were pretty nicely made, so in all that area doesn't need changing. I found the controls a bit of a pain, because I was partly covering my screen with my finger when I was moving upwards. I didn't realise at first that I was locked to 3 'levels' of height. I played several times and was expecting the levels to change, but it didn't.
I'd recommend the following:
1) A new control system would benefit the game - you could slide with the touchscreen to move the ship about, or even consider implementing the gyro features that smartphones have.
2) Remove the 'rails' that we run on. I felt quite limited, as if I was on rails or a track, so only had 3 real degrees of movement. Let the player move freely up and down (and perhaps backwards and forwards slightly?)
3) Enemies/obstacles/pickups! I'm not sure how you'd fit this into your storyline, but some sort of enemies would be fun. Ships coming towards you shooting lasers, bombs, missiles etc that you have to dodge. Maybe introduce bigger lumps of rock that take up half the height, or ones that block the path, which you have to shoot to destroy (smaller rocks come flying at you?). Even consider pickups: health, ammo, armour upgrades etc.
I see that these are big design ideas, but I think it'd help make the game more interesting to play. Consider looking at the game 'UN Squadron' for the SNES - I feel that has similar game mechanics and you could find inspiration from that.