I am seeing the relevance of sakiori weaving to other weaves that the warp and weft are not equivalent. Usually the warp threads are finer and set denser while the weft threads are sturdier or bulkier, giving a general ribbed finish. In some case, the finished surface is warp-faced and the weft is not visible, such as in Grossgrain ribbon and ottoman fabric. Warp threads make up the color and pattern while weft threads, in some case cords are used, provide strength and durability. In the case of sakiori, by using fabric strips and regular threads, the contrast between warp and weft is extreme. The warps are not covering the wefts and instead the technically underlying weft weaves are visually dominant.
If you are using a pin loom, in that case you have equal numbers of pins in both directions, you have have to make adjustment to increase density of warp threads. I don't have experience with that but I imagine you could add additional spacers to hold and separate multiple warp threads. Warp will also have greater length reduction so you will need longer yarns that add to complexity of organizing and tension control.