Our system has a water bladder that we put underneath the truck which acts like a staging area. We have a little compartment for it next to the stairs for it. The filters don't necessarily need to keep up with the showerVerify that your filters are "absolute" and not "nominal". If the latter, you will lose efficacy.
You may struggle to push shower water, circa 2 GPM, through a 0.01 micron absolute filter or nano-pore carbon block. Have you considered a two stage system? Get 90% of the junk out, recycle the water to finish your shower, then on a slower pump rate and/or with a finer filter, treat the water before it is dumped back into the storage tank. At this point it is better than potable tap water.