I realized that you can see the carried floats on both sides??
You don’t mean you actually have floats on each side do you? Are they just sort of bleeding or peeking through between stitches? That is pretty common, especially with high contrasting yarns. I don’t usually weave in the floats but try to just knit across carrying the colors without weaving. If you only have 5 stitches between uses of a color that is the best way IMO to keep that from happening. But sometimes you have to carry further than that. Sometimes you can change the design a bit so that you don’t have to carry the colors more than 5 stitches, even if it means adding a “fleck” once in a while of the color that is being carried.
If you are going to do the weaving though I don’t really know how to prevent it. Keep things loose, but you are doing that. Maybe someone else knows. Good luck.