To me, feet first running is just that...running with your feet first, not your shoes. Of course, "they" always want to advise we run barefoot after taking our shoes off, doing short drills, blah, blah, blah, but if you want to really strengthen your feet, lose the marshmellows and just run barefoot.
Feet first running
Triathlon Magazine Canada (blog)
Loosening the feet before every run is an excellent way to improve foot ... Spend four to six weeks incorporating easy race flat and barefoot running ...
