I would very like to avoid relying on such trick, and rather use functions than methods. That would simplify greatly the parallel code.

If I look at the two methods that you need to do parallel computing on (_count_new_vocab and _count_fixed_vocab), they 'self' only once, that is to build an analyzer. The analyser could be built outside of the parallel code and passed to two functions that contains pretty much the inner workings of respectively _count_new_vocab and _count_fixed_vocab. These function wouldn't need to be a method, and the problem is solved: the design is simpler and does require pickling tricks.