You don't want soluble nutrients, because as you have discovered, you can't hold onto them. In sand, you want to hold your nutrients in crop residue that decomposes at different rates. The best potassium fertilizer out there is a heavy high carbon crop residue like rye or sorghum. First blast of rain will wash out a big chunk of K from that residue after it's dead, but it will still hold a bunch, and release it as it decomposes.
Focus on covering your sand with vegetation first. If it's not working now, put it into sorghum now, or write it off until it gets cooler in the fall, and then flip it to rye, a clover, chicory, plantain, and ragweed. Let that rye go all the way until it's done the following year, and then roll it down if you can. Keep the big duff, and that sand will perform for you.