It seems that group-ride speed has become your primary objective. As others have said, a road bike is your long term, ultimate solution. In the meantime, ride what you have and save your money for the new bike; the cost of modifications and accessories for the hybrid will quickly surpass the down payment on a new bike.
One inexpensive addition to your current bike that will add a lot to enjoying it is bar ends. The additional hand positions provided by long bar ends will enhance comfort and fun far beyond the cost.