powered trailer hill climbing
I live in the flatlands of Illinois & can gear for speed. The trailer never slipped even in gravel, partially due to tall gearing, but also due to using the seatpost hitch position. Precisely when you need it, you get extra traction when accelerating or climbing since the wheel is "tucking under" to some extent. In other words it increases its traction by pushing upward toward the seatpost. It is probably a small effect given the shallow angle involved, but I never had a traction problem.
Stuart Brandt has a Comet CVT on his 3+ hp powered trailer and has a low overall ratio. He climbs steep hills, accelerates quickly and still has no traction problems except perhaps in gravel with excess throttle. You can see YouTube videos of his working well on grass. His hitches to the seatpost like mine.
Interestingly, the trailer works best with just enough air pressure to keep the sidewalls seated. It appears fully inflated but absorbs bumps better and probably gets a little better traction as well. I used the trailer a lot and never saw any hint of tread wear. The curves in the tongue filtered out vibration. No vibrations were transmitted to the bike, which was quite a contrast from the FWD I built first.
I strongly advocate powered trailers as a simple, easily built, versatile means of motorizing a bike. The only problem with a minibike wheel version is the lack of a freewheel which makes it difficult to tow when the engine is not running. That appears to be a weakness of the Third Wheel powered trailer as well. Since there's so little weight on the wheel, a 12.5" or 16" rear bike wheel will work just fine, solving that little problem. Make one with a derailleur or geared hub & you have everything you could want except bump start.
I don't recommend a CVT unless automatic ratio reduction for hill climbing is a higher priority than partial throttle cruising and fuel economy.
If you build a single wheel version, keep it rather long and low so pendulum effect will help keep it vertical. Imagine a line from the hitch to the tire's ground contact patch and keep more weight below that line. Make sure the wheel is aligned with the hitch or it will "dog walk" and tend to rhythmically sway laterally under power.
I wouldn't want to build a 2 wheeled version, fearing it would have to be too wide to remain upright in fast or tight turns. I wouldn't want one wheel on the road and the other on the shoulder when trying to keep to the right as far as possible.