ya - forgot to mention that you want to stay far far away from the wet clay. A tiller plugged solid with clay is something you don't want to experience.
I'm even thinking about a tiller for myself, somewhat in the same boat as the neighbor only my tractor is a little bigger than his. It comes down to $2500 for a tiller or $6500 for a JD 3020.
If the plow works ok and all you are lacking is traction, try tire chains on the tractor. Cheaper than another tractor or tiller and you can always use them in winter in the snow and ice where they really shine. If you can find a good set of used ones, and are unhappy with them, you can always sell them again and be out nothing.