A broken used Chinese scooter in the 125cc range can usually be had pretty cheap. Usually from what I have seen if the motor makes it a hundred or two miles it will hold up for a while. But the chassis is pretty much always crap so expect to see terrible wiring, bad bearings and broken welds. That just means it will be a good price and still work for what you want it to do
Find one with the motor and all of it built into the rear suspension and it would be easy to cut away all the extra frame junk and make a u-joint hitch for it. I guess a rc car servo could be used for the throttle and connected to your existing electric throttle. I would probably just forget about the scooter brakes since your bike brakes should be ok. If you have a servo system for the throttle a trailer plug could get everything working. Park/brake light, start, throttle, and ignition kill would be all it needs I would guess.
The motor is pretty small so if you do fiberglass or whatever to make it aero it would also give you some storage room. I am not sure how much air it would need for cooling but that can be figured out from how much it gets from the existing scooter body.