Blikbok,
I had an issue with the Pilas as well, in my M3. I should have mentioned this, but didn't think about it until you posted. It seems that the Pila cells are just a little fatter than 123's and therefore do not fit inside of the spring on the Surefire lamps. This causes the Pila cell to push the negative spring up and prevent it from making contact. There are two ways around this that have worked for me.
The first is to open up the spring on the lamp with a couple of pairs of pliers allowing the batt the go inside of the negative spring, thus allowing the spring to contact the body as it needs to.
What I did was to get a spring that the batt would fit inside of and wind this spring around the Surefire negative lamp spring so that you have a dual spring setup. It acts as a bridge between the body and the Surefire spring. My DMM shows no resistance using this setup and it has worked for me.
If you can't find a spring, I'm sure that an email to Pila would remedy this. I am using the Pila spring that is supposed to be used on the Pila 3.7v lamp to make it work in a Surefire 6P.