I've had a vibration that would change between off/on throttle. This was due to low transmission fluid. The transmission rear output shaft seal can go bad and leak. Just something to check.
I also have a short throw, Steeda Tri-ax, and it does vibrate more than the stock one. To check this slip the leather shift boot down. The stock is a circular black metal, a Steeda Tri-Ax is a polished rectangular shape.
On the wheels, they could be out of balance or bent. I have bent a bunch of wheels, I currently have both fronts bent I believe. The new edge doesn't have the greatest ride from the factory. The tires you currently have have a taller sidewall than the factory size 245/45/17, so they should ride a touch nicer depending overall stiffness of the tire - taller sidewall means more flex. The tires probably aren't contributing a lot to the ride stiffness over factory. The springs though, those can make a world of difference.