It's not even "think", they just are. In a recent Switch trailer which showed short clips of Octo Expansion, one of the Special only stages can be seen and the UI clearly indicates an infinity symbol next to the special.
As for Baller, what I'm expecting is, you can't explode, or explode results in an instant loss/splat, same would probably go if the Baller were to break at any point. Because more likely than not, the level which has infinite Baller is an obstacle course designed around the Baller's mobility and not any combative property.
And I don't really see an infinite Sting Ray being a thing, unless the particular stage will act more like a stationary turret shooter level.
And yah, the Specials will probably always be their most up to date version, if Octo Canyon is any indication.