I need to re-use the same sound effect that repeats and overlaps. For each sound to be able to play overlapping with itself (but with slightly different start points), up to 3 times would I need 60...

What you need is more like a "sample" player. Yes, 20 sounds up to 3 times (so 60 sounds playing simultaneously) would require 60 instaces of the SuperpoweredAdvancedAudioPlayer. That may be too much.