You also need to ensure that C-channel bumper can handle the dynamic loading that is going to happen when travelling and going over bumps.
With very little additional weight, a 4" square bumper shown below fell off in traffic.
And the original post
here.Even if you tie into the frame to the point that the rear bumper isn't even required, there's going to be significant force being exerted that could bend the frame and/or bumper and produce a moving projectile sent at drivers behind you when the scooter comes loose.
EDIT: I see now your other thread on the fabrication and construction of the hitch support. I still would be very concerned in following behind that while under load. I would definitely test it on a low-traffic area and then look for any stressed and buckled areas of the frame.
Whenever I've added weight behind my axle, I've been sure to add an appropriate amount of weight to the tongue to balance it. In one instance, I have had instability and sway due to what I would consider a very small amount of weight. Pulling over and moving about 60 pounds inside of the PUP from the rear to the front made it stabilize.
Please prove me wrong but this looks like a recipe for damage.