Dunno if it quite fits the problem solving part, but Megaball has always been one of my favorites for low-end Amigas. The shareware version of 3.0 is on Aminet. Despite being called MegaballAGA.lha, it will work on ECS. Music is in a separate archive, MBmusic.lha.
I highly recommend picking up 4.0. I think it's still available in some incarnation...