I did some welding this weekend, and attached two platforms to the sides of the trailer fork. These will support the batteries, to be bungied on top for now. Eventually they will hang underneath the platform, and it will be a shelf for carrying whatever load I need. I decided to invert the fork (mount it on the low side) to keep the mass as low as possible.
My first test run was today. I got the controller strapped on, batteries wired, and bolted the contraption onto the bike. I started with the 26" brushed geared Heinzman wheel, and took a couple of laps of the driveway. I found that over 10mph, the trailer would wag back and forth pretty severely. I could hear the trailer-bike connection rattling as the side to side motion translated to front to back motion on the connecting bolts. I added a couple of spacers and cinched it down tight on both sides. This removed the front to back play, but the joint would still turn to allow for pitch changes. There was a vast improvement in stability. However I could stand next to the bike and when I grabbed the seat and shook side to side, the wheel itself had play that contributes to the wobble.

I took it out on the road, and there was instant smilage! there is nothing like the feeling of a light pedal speeding you up a hill. The bike was steady at 15mph on flats, and would slow to 12 up hill, but I was pushing 750W if I did not pedal. The motor did not heat up to more than warm. There was more noise than I had hoped. It was like a big model airplane following me around.


I then swapped out the wheel for the 20" brushless.

This motor is dead silent. It does not have as much torque, but seems to be able to hit similar speeds. The silence is amazing. The smaller wheel seems to be more stable. Possibly since the weight is 3" closer to the ground, and the wheel is a lot stiffer side to side.
I'm considering whether to make the effort to make a trailer that is 6" shorter for the small wheel. I want something as compact as possible, but still stable.