Helen,
I'm not sure whether American possums have the same preferences as Australian ones but a quick and cheap temporary drey (nestbox) can be made with a pair of plant hangers, of the sort that have a wire-frame bowl lined with a coconut-fibre lining. The ones that are about 60cm (2 ft) across are the go.   Join them 'face-to-face' and make a hole in the frame and lining, at the perimeter, large enough for the animal. Fix the drey in a tree and any Australian possums within cooee will be colonising it within a couple of days.

I can't say about American possums but Australian ones (brushtailed ones) have quite large territories and would need to be removed more than 5km before they could be released into territory they hadn't already 'mapped', allowing them to run back in a couple of hours. Most suitable habitat is already full of possums to its carrying capacity so releasing them 'out of territory' is most likely going to result in a death that you don't witness. Installing a nestbox outside your house removes the immediate problem without killing the animal and is effective so long as you've got all the entrances to your house blocked to prevent recolonisation.

And, given all the stories in the postings above about deadliness, I reckon Americans who describe our wildlife as dangerous have a bit of cheek.

Cheers, Rowan