2x3 tubing is more than 3x as resistant to bending as 2x2 tubing. In fact, you could reduce the wall thickness a bit to drop the weight and still have a much stronger beam out of 2x3. I'd cut the floor and use the big stuff. Besides, 2x3 matches the existing frame stubs pretty well. If you spend a little time on it, you make it look as if there is a full frame under the car.