I will get flak for saying this but frame notching will reduce the rigidity of your frame by half. The rigidity of box beams is determined by the size of the cross sectional area of the beam. Reducing the cross sectional area like with frame notching reduces rigidity. Moreover, frame notches often require 90 degree joints which are stress risers. The proper way is to move the frame rails inboard while maintaining the same size of cross sectional area.
Welding reinforcing plates on the sides doesn't do much good as its the top and bottom sides that provide vertical bending stiffness. Cut the top and bottom sides in half, you lost half your up and down rigidity on the axle hump. Now on a nice flat and smooth race track this loss of rigidity isn't as much of an issuse as it would be on real roads with bumps and potholes.
Besides all that, performing major frame modifications such as boxing and notching frame rails really requires a chassis jig to kerp the frame straight and square. A typical paved driveway or garage floor is nowhere near flat even for accurate measurements. Even then careful back step welding techniques should be used to avoid heat warping your frame. Too much heat at once and your frame warps, requiring a trip to the chassis rack machine.