I solved the problem of the projectiles colliding with the shooter when fired by assigning a different CollisionCategory to each. Then, I set the growths to collide with everything and the shooter and projectiles to only collide with the growths. So, now that works nicely.
It took a bit longer than I expected, so I will pull out the old collision code and create the new collision code tomorrow. I also need to either create a barrier around the edge of the board, or to destroy anything that goes outside its bounds.