Grow power in Wisconsin uses wood mulch. Good for walking and the slow decomposition of the wood helps heat the greenhouse.
My floor is concrete and after finding out that it absorbs heat well would not put anything over it. As for spills, they dry up quickly anyway from the heat. It is also easier to keep things better stabilized and level.
Wood mulch would be a great place for all kinds of bugs to breed inside your greenhouse. I'd stay with the bare concrete slab. Perhaps seal the cracks with an epoxy concrete crack repair sealant. Consider an epoxy coating if maintaining a clean slab is important. Light colors will enhance light diffusion, if much of the floor would remain uncovered.
Greetings from Wisconsin!
My take is that as long as nothing structural is sitting on the river rock you'd be fine to use that. Might help keep the floor from getting slippery. But you'd also be fine without.