to one thing I can answer I think ( hope Immy won't disagree

The Alligator and the A0 or eWaves are not really different things.
The gator are smoothed MAs with period 5, 8 and 13. If you look at the ópening between blue and green, it's 5-13.
The former A0 was 5 - 35 ( according to the manual ), so just a little smoother or - the other way round, gator being a little quicker regarding the blue line. I don't know, if eWaves is exactly A0 on that, but sure not much different.
And gator has the red line of course.
The most important difference is, that the gator gives you comparison to PA and A0 gives you the structure.
Hope it helps a little on that.
Bettina