muddy yard due to dog, hates paws wiped.

Question
My black lab who I swear is part pony is almost 2 years old, very tall and leggy at 92#.
He was rescued at 6 mo.underweight and with worms. Now he is robust, very verbal and mischieviously adorable. He crates well while I work but he has torn up my backyard and now gets so muddy. He ate the wooden back door to the garage and dug under the fence to go visiting. I had to install a runner line to keep him safe. I once had a sweet green backyard and now it is a mud pit with huge holes and muddy watter. He hates his paws wiped and cries like he is being murdered even though we do this frequently.
While my grass will never grow again, would straw or mulch help keep the yard cleaner?
I love my dog even as he has ruined my backyard, but I cannot seem to keep the dirt out of my house. When it rains, I dread letting him out to potty knowing the mess I will have on my floors.
Straw or mulch or more diligent paw washing?

PS He REFUSES to get into bathtub when I try to give him a bath (however, I frequently see his paw prints in there later- sneaky bugger). Bath time is swim in nearby pond. But he has started cleaning himself like my cat.  

Answer
Labs!  I don't have a solution to this one either.  Straw does help.  I have a friend that has a small mulched fenced area.  She mostly has Shepherds though. I also worry about the dog eating the larger pieces of wood.  I have about a 50' x 50' area fenced.  I keep struggling trying to grow grass.  I posted a question this several years ago on the old AskMe.com back when it still had some good people.  I never saw any of the suggestions as workable.  Mostly it was keeping a hose handy, and hosing their feet off.  Some people use a hair dryer to dry the paws.  With him tethered, you could at least keep the hose where he couldn't reach it.  I had to make several changes when I went from using a tether to the fence to protect newly accessible things.  I also lined the fence with flagstone to prevent digging.  

In the worst mud, I sometimes use a tether out front where grass does grow as long as I don't put the dogs out there much.

As top dog, you can insist on wiping his paws.  I even dip them in a bucket of water first sometimes when the mud is the worst.  The dogs see all the
people and dogs in the household as a pack with each having their own rank in
the pack and a top dog.  Life is much easier if the 2 legged pack members
outrank the 4 legged ones.  You can learn to play the role of top dog by
reading some books or going to a good obedience class. A good obedience class
or book is about you being top dog, not about rewarding standard commands with
a treat. Start at http://www.dogsbestfriend.com/