I bought the bike with a Classic Industries hitch on it. I'm going to do a mod to the hitch, in particular the suppoort straps that go up under the back. IMO they are too weak and I can feel the hitch moving side to side at times.
I have a Classic Industries hitch on my 1100 and I pull my "I-Lean" one-wheeled trailer. I too feel movement in the pegs with the trailer attached.
If you examine the foot peg mount assy, you'll note that it is attached through rubber bushings to reduce vibrations to your feet. With the hitch attached, this allows the whole system to float about a bit, thus letting you feel the inputs from the trailer.
I don't think reinforcing/redesigning the rear straps will make the movement go away, though it may reduce it. That would require removing the rubber bushings and replacing them with something more solid, either a hard nylon or aluminum/steel spacers.
I would be concerned with mounting the peg mounts solid though; these are long cast aluminum parts that might be stressed too much if they were solidly attached.
I've been watching my peg mount closely, checking for sighs of fatigue. I haven't noticed anything to date. I have not pulled the assy off yet to inspect the bushings but will probably do that over the winter.
Just something to consider....