I am currently doing this with a Whismur that has evolved into a Loudred and will very soon be an Exploud (although I used a Mudkip/Marshtomp between Littleroot and the Rusturf Tunnel.) However, I'm a little too far in to post everything that's happened without it just being a generic walkthrough.
When you say Mudkip through the whole game, though, do you mean instead of eventually having a Marshtomp and then a Swampert? Your listed rules don't actually state that the pokémon is not permitted to evolve...