I built this minimal push trailer nearly 20 years ago. This short video is all that remains of it except the hitch.
http://www.youtube.com/watch?v=XjEgsKqfi74
Use pause when watching the video to see it a little better.
It worked just fine. No need for it to be any stronger or heavier. It seems a shame to pay for, then throw away most of a minibike frame when it's so simple just to use a few bolted pieces of angle steel (mine was from a discarded bed frame) to attach the engine to the wheel. Nothing had to be welded. It only has to be substantial enough to support the weight of the engine, not a passenger.
The 'u-joint' hitch does not have to be as precisely built or as strong if the trailer stands vertically on its own by the pendulum weight of the engine. That's why mine seems a little longer than necessary. I needed to lengthen it a little to get more of the weight under a line from the seatpost hitch to the contact patch of the tire. (SEE ATTACHMENT)
The extra length also placed the engine in the middle between the hitch and contact patch such that the small flex of the 3/4 inch electrical conduit tongue stopped the trailer from bouncing as much.
There is no need for more tire pressure than is necessary to keep the bead seated. The stiff sidewall keeps the tire in shape and the low pressure helps the trailer absorb bumps in the road. The low weight and low pressure nearly eliminates the possibility of punctures or even tread wear. I can't understand why anyone would prefer a foam airless tire. It's been reported here that they wear quickly.
I can understand cannibalizing a minibike if it can be obtained cheaper than the sum of its components, but it seems to me that you should keep the frame intact so you can sell it to recoup some of your outlay.