Very creative idea, I like it, but I don't think there will be a gain in performance.
I think there will be considerably more chord wise drag from the billow of the triangular cell because it will inevitably taper. A rectangular cell's billow runs straight from the LE to the TE.
I also think there will be very strange things happening on top of the leading edges of adjacent cells, since one will have very little span to the next rib, while the following one will have much more span and thus ability to deform.
The way I see the goal of internal strapping is to keep the overall wing shape, surface area, and profile stable through changes in internal pressure (AOA, speed, etc…)
Without internal straps, changing billow alters the span dimension. I agree triangles are good, but with flexible material they only work in tension. Therefore, without straps, the cells will still bulge, and thus affect overall shape, profile, and surface area. If you have to add strapping, you are back to the beginning again.
I also think it will add exponential complexity to the construction. Triangle cells will only touch rib to rib at one point on the top, and one point on the bottom. So instead of a top skin and bottom skin, you have a nose skin and a tail skin. The tail skin will have to split into a top tail and bottom tail if you want to close up the kite with the trailing edge as the last step in the typical way.
Cool idea though, definity worth modelling up in 3D to see at least what it looks like and how it would affect construction.
I've always thought a molded wing would be cool. Imagine squirting a thin layer of something like hot glue between two layers that are then pulled apart into a two sided vacuum mold, so the inside is filled with billions of hairlike strands giving the kite/paraglider/wing/whatever a perfect shape.