Honestly, in a tiny house, I would surface mount all the plumbing to make it easy to work with/modify/expand.
For style points, use copper.
Again, this is what I did so obviously biased.
we think alike...i am going to surface mount the electric as well. i am going to hang it all under the floor like in industrial setting with pipe hangers too.
i think its dumb to build a wall to code and then drill holes in it for wiring and plumbing...its like giant termites to be honest. a 2x4 with holes drilled in it..really !...lol...i dont know what walls will be but 2x6 minimum for me.