Having dispatched nearly 20 of them by hand with the Swiss army knife I'm holding in [link|http://www.aaxnet.com/images/ajg11.jpg|this photo], (generally at about 3:00am) I know a fair amount about possums.
Thinking a wiffle bat would get a possum's attention is a complete misunderstanding - Sammy Sosa's corked bat swung by go'vner Arnold wouldn't get its attention. Those things are tough. They feel like a deflated football with some jello and loose chicken bones inside. You can't get a knife through them and they're just too stupid to know they're dead - and yes, they'll just keep right on eating. They don't "play possum" either, they snarl and snap and try to get at you any way they can.
The state possum expert (It's illegal to be a possum in the State of California) describes them as "working with about 1/3 of a deck". The first time one got into my pigeon coup, I disciplined it vigerously with a 2x4, but it was back 10 minutes later. they're too stupid to retain a lesson, so all you can do is kill them.
They're plentiful though - they're just too ugly and disgusting for any self respecting predator to want to get close enough to to kill one - and who'd want to eat it?