1+ for drilling from the tailpiece mount. I think this is the way the strings are grounded on most hollow body and floating bridge guitars. Takes a long bit, but it's the simplest of your ideas and the most tried and true other than pulling the bridge post...which as you say is mightily stuck.

[edit]...although when I was posting I had not seen Simon's last post. Of course, if there is an opportunity to buy a new tool that changes everything ;-)