Would work best as a single season anthology series. It needs to set audience expectations and let everyone get comfortable with the formula. When the audience has been trained to accept the rules, it can start bending the rules, then break them in the last episode or two. By the end he's moving between episodes we've already seen and maybe even running into "future" episodes which will never actually exist.
This also let's you hint at an actual character and motivation for our narrator. Who would expect the narrator to get an arc?