Its a shame the 'low carb' diet had 30% carbs in it. Hardly a fair comparison when low fat diet only had 7% fat. I think every high fat/low carb advocate would laugh if told low carb diet was made up of 1/3 carbs!
How can the data from a 12 day diet 'suggest long term fat loss' from any type diet?!
You do have a rare foot type; then again so does everyone - despite all the marketing and hype to help sell trainers - EVERYONES foot is unique.
The ideal shoe to run in is the one you feel most comfortable in when running. Unfortunately its not the quick fix answer everyone's looking for and its why the simple Overpronator /Neutral/ Supinator marketing model has become so popular.
Have you run in VB long and have you run in them without getting injuries? In my experience overall running style & posture and hip/leg flexibility matter much more for injury prevention than what shoes you're wearing. Unless you've been running less than 6 months, in which case i'd recommend a more supportive, cushioned shoe.
Is it only a sharp pain when you flex your lower back (slouch or bend forward)? S1/L5 disc is just above your sacrum, but a lot of people have narrowing at that point so doesn't necessarily cause any problems.
If stiffness came on gradually while running chances are its your lower back muscles that have stiffened up, putting pressure on the spine at that sore/weak point. For now get some heat on the area and find a comfortable position to rest - either lying in a hot bath or with hot water bottle on back with knee supported over cushions or a chair.
Gentle stretching of you gluts (knees towards chest (1 at a time) - without pain) while lying on your back often helps. If no better by tomorrow book in with someone to get it assessed - a sports physio would be best
ITBS that get tight after high mileage is normally caused by weak/tight misfiring glutes. Your ITBs are getting tight to compensate for them. When tight they can 'pull' on the knee causing the knee pain.
Running on outside of feet could also be a clue that your gluts and/or pirifomis muscles are tight. Get massaged & stretched by sports massage therapist.
Substiuting running mileage with glute strengthening routine (lunges & 1- leg squats) should help. (I did same when training for my first marathon) You can feel a big difference in two weeks so worth starting now.