So many approaches, how true. It sounds like you are going the two wheel route. If you are, be sure to have the ball on a rotating mount. The ball doesn't really have enough motion to cover the lean angle of the scooter without it.
My concern was with my trailer the trailer's maximum lean angle. The hight of the bottom of the trailer from the pavement set the width limit. If I went much wider I would start to interfere with the lean angle of the scooter. In my case they claim a 55 degree lean angle and the trailer can do that at 17 inches wide. I haven't scraped the edge yet but I know I have come close.
There has to be enough "rotation" with a 2-wheel trailer hitch... Witness; that CRUDE yet EFFECTIVE Asian home-built setup pictured! One of the most simple, but effective setups I've seen is a universal-joint, THREADED onto the scooter so it's not ONLY a universal, BUT can rotate as far left and right as needed, on the threads.
I also do like the single-wheel design like yours. I've been looking at the bicycle single-wheel trailers, and can envision one like that, with the wheel trailing off the rear, with a coil-over shock. With the "load" being slung BETWEEN the scooter rear-wheel, AND the trailer "tail-wheel" it would be well-suspended and should track well.
Both single and 2-wheel designs have their own particular good points. Like I said, if I do make a trailer it will be somewhere down the line, but the idea certainly appeals to me! A fellow on eBay is selling a Vespa 2-wheel "trailer" made from a side-car, to actually seat a passenger. It looks fabulous, but I'll bet it violates numerous laws...
I guess come spring, I'll have to check out that edger carcass better and see just what kind of thing it might "morph" into... LOL!