That's a tall order, and being that I'm so steeped in Hassidut (whose overarching principle is to always be happy) I feel compelled to offer a couple of explanations of the discrepancy:
- When one is involved in a mitzwah, one is (temporarily) not required to perform other mitzwoth. Perhaps the deeper reason behind this system is that as we know of the world, everything is connected to everything else. So, as long as you are involved in a mitzwah, then you can be happy because the performance of any mitzwah has an aspect of fulfilling all mitzwoth.
- The Ohr HaHayyim goes on to say that Chazal say one must be happy in order to pray. Since an aspect of Hassidut is to be in a constant conversation with God, so the everpresent nature of this prayer necesitates an everpresent happiness. Perhaps it is for this reason that it is said, "it's a very big mitzwah to be happy always."
Either way, there is still a real need to learn and perform all of the mitzwoth which HaShem commanded us. Each one is a priceless treasure and the deepest means available with which to bind oneself to the Life of All Worlds, blessed be He.