Katie continues to have off and on mystery lameness. However, I think I am finally certain it is a toe causing the pain. Recently, the toe in question started to bleed as if there was an abscess. It is a middle toe with an amputated neighbor.
Initially, we dismissed the swollen toe because Katie refuses to flinch or wince during an examination. The toe's joints are intact and tight. The vet and I tried to pin point the pain, but inevitably she would put her game face on and be as sound as an old, neurological dog can be. She also has toes on the opposite foot that are completely broken down (see below) and she does not complain about them. It was hard to believe she was complaining about a swollen toe. 
Katie was put on antibiotics. I think she is possibly better, but she continues to not be forthcoming with information about how much pain she is or is not in. I am tempted to X-ray it, but then what? Would we take any action? I have to admit I would love to see an X-ray of both rear feet, but I hesitate because it would be stressful and she would most likely have to be sedated.
Recently, I noticed a deformity as I was examining pictures of the injured toe. In the photo below look at the position of the nail and the pad (see below). The pad should not have an angle in the middle of it. The nail is also on the same plane. If you compare to the other toes (see above), you see that the nails run parallel to the pad, but are not on the same level. It appears to me that she is wearing the nail and part of the pad away. I have never seen anything like it and I am not sure what would be happening internally to cause it.
Despite it all, Katie continues to be a happy, playful girl.
This Little Piggie was deformed,
This Little Piggie was dislocated,
This Little Piggie was broken,
This Little Piggie was amputated,
And this Little Piggie went wee wee wee all the way home.