The nature of the JRR quilt is that you don't know what you will get until it's done. I suppose it might be possible to figure out at least roughly which fabrics will be adjacent to each other, but it boggles the mind. The beauty of using a jelly roll is that all the fabrics go together, so that means the final product should be pleasing. I think your plan of alternating strips is a good one, but you may still wind up with a lot of reds against reds and whites against whites, and I think that's okay.