I think I've shared this idea on a discord server before, but thought it would be relevant here.
I feel like conjugated 5-style might be a more feasible approach to solving 4 pieces at a time.
Imagine using conjugates like in ayam/eka to set up a 5 cycle. It would be more like ayam since you are setting up 2 pieces, but then doing a subset of 5 style (with less algs than 3 style) to solve 4 pieces, and then undoing your setup moves.
It is less algs than 3 style and solves 4 pieces at a time, but the conjugation step is slow for setting up 2 pieces. I think that the best way to do it is just to do 2 3 style algs.