Following the pattern I already established, I reworked the shooter to use the Farseer physics engine. Since I have all the objects sharing the same base, and I've already re-factored it to do most of the physics stuff, it was mostly just a matter of making sure the old things weren't being called any longer and that the new properties were being set correctly.
I still need to disable collision detection, since all the objects in the game correctly collide with one another. Because the projectiles collide with the shooter when fired, sending the shooter flying about wildly, I'll either need to recalculate where the projectiles are generated (so that they no longer originate from the center of the shooter), or just create other collision groups and make is so that the group the shooter is in doesn't collide with the group the projectiles are in. I am leaning toward the second, since it should also help with processor time.