Solution: two chains. One white, one black. Use a road double up front and put two single cogs from a cassette on a rear wheel with a freehub body (with spacers as necessary). If fixed, weld the freehub in place. If for a single speed, use a White Industires Dos freewheel (or the freehub setup). Cut each chain to the necessary length.

Or, better yet, shifters + derailleurs + ride your bike.