Programming string light chases

I am playing on an event with 8-10 ish stringer type of things. They are 24 lamps per string. All strings start at the same place and more or less end at the same place. Stringer one starts with number 1 and ends with number 24. Stringer 2 starts with number 25 and ends with number 48 and so forth. I have made groups for each string. I am wanting to make essentially a look/cue stack that can have the effect of some type start at light 1,25,49 etc and work its way through to light 2, 26, 50, etc.

Easy example is lets say all the lights are in blue and I want a white look to go through so cue one would be saturation out in 1, 25, 49 etc. cue two would move to 2, 26, 50, etc. so I would end up with 24 cues.

I guess my question is there a simple way to build this stack? I have been playing with the effect engine and can get similar results but they are effect engine results. My next guess is to make groups 1/24 or so, then make that way? Any other thoughts?