I don't own a gbaamp but I think this is the .nds.gba file that could be used in this configuration.
For the topic about the number of background, there is 20 different background I think but you can add as many backgrounds and level as you want as background are jpeg file, levels are text files (can be produced with the frozen bubble level editor) and these files are contained in a gbfs image.
I will provide a tutorial soon explaining how to mod the game.
But it can be done now if you get the source and if you some computer skills (essentially produce a new gbfs image and link it with the binary)
Hope this helps ...
PS: I've attached the zip containing the game to my post, I hope this is ok now for the game registration to the compo?
Have a good day,