OK, I guess that we do not go there... I was thinking that you might mean the 'stop' moment with half the kites in a 'leading edge up' moment.
I think that you have to at least go through there in doing your working with phantoms Grand Swing Thru. Half way through each Trade (180 two kite pinwheel or whatever you know it as) each 2x4 will have to become a 1x8. In the 4x4 matrix that you star with there will be a conversion to a 2x8 then a 4x4, then whne the phantoms come in a 3x8 finally a 6x4. The 3x8 will consist of two 1x8 formations with 4 phantoms and 4 real kites and one 1x8 formation of 8 real kites.
Under normal conditions what is the limit of kites on a vertical orientation tip to tip? I expect the opportunities for 16 fliers are not that common so the need for some standardisation is required so that everything can be quickly conveyed.
I really do hope that something can be transferred from the square dance world that I know. We went through the standardisation stage in the 70's and 80's. I suspect that there might be more mileage working with 8 kites in a 4x4 matrix with 8 phantoms that are used when required. I will try and spend some time thinking about possibilities that do not turn lines into a rats nest.
Thinking about your "Sprocket figure" as well as it being an asymmetric exchange the diamond it is also very similar to part of a traditional dance Venus and Mars where you have right and left hand stars that cross over and cross back eventually leading to a promenade which I think you would call a 2x2 pinwheel? I need to have another look at the matrix/grid flying manual.