After much sturm und drang, I got a pair of sissors and clipped the tie. He still wouldn't move so I put a basket and cover over him to allow him time to recover.
Meanwhile, Husband had called Mathews Animal Control, which is manned by compassionate people who actually care about animals. That is some definite progress in these parts. I commend them with extreme praise.
On arrival, Mr. Horne (the Animal Control Officer) picked possum up by the tail, unraveled the plastic tie, and put him under a bush. He headed for beneath our deck, with his poor testicles conspicuously hanging low, and prepared to return to normal or a little less.
We haven't seen him since, but Mr. Horne says he'll be fine but will probably be cured of his desire for sex. I, for one, can live with that. I left him a little food in case he gets hungry.
And life resumes on Waverly Lane.