I've had very similar issues. When I first began barefoot running I didn't realise that although I'd naturally adapted to a forefoot landing, I was still overstriding in the same way I did when I was a heel-striker in marshmallow shoes.
I was also overstraining my calf muscles by running 'on my toes' and never touching down with my heel. I had nasty shin splints and had to take a long break from running.
I've since learned that a key part of good form is to make sure you land with your foot directly underneath you, not out in front. Lean forwards slightly by bending at the ankle (not the waist), land on your forefoot or midfoot, then lightly touch down with your heel and push off.
The other key is to go very slowly at first and build up speed and distance extremely gradually. Listen to your body and pay attention when it complains!
I had been running completely problem-free for several months, then a couple of weeks ago I built up both the pace and the frequency a bit too much again. Combine that with going for a run when I was very over-tired and stressed one day, so my form got sloppy, and hey presto - shin splints again!
Barefoot running isn't easy, but I remain convinced it's the way to stop long-term injury. It has an honesty about it - you soon find out if you're doing something wrong!