Rabbits will bite through chicken wire.

Had that happen...
I made rabbit sausage this year. The secret is that rabbit meat is dry and rabbit fat is bitter and gamey. So you cut it with fatty pork belly. We made ours with about 1 part pork belly to 3 parts rabbit but it did not grind smoothly. I suspect more pork belly would allow it to grind smoothly. The stuff that did grind smoothly was perfect. The stuff that didn't was chewy but good.
You could probably use chicken or beef fat instead.
We made breakfast, links, and itallian. It was very good.

Very lean. Almost no fat came out when it was cooked, but it didn't stick.