Ahh, good, didn't know others out there were also on the same wavelength.
We started doing it 3 years ago or so and the initial play was to scan them onsite, but that turned out to be pathetically inadequate and the plan was changed mid battle on judging day. Instead, Fletch, out brewgyver has access to one of those wunderbar "document center" machines that takes a stake of papers and emails pdf's.
The process is entirely woefully manual at the moment, but I think we're at the point where we've learned enough to figure out how to automate it better.
We went with hosting the files on the web just to avoid the hassle that comes with emailing a chunk of pdfs to people.
And yes, my dream would be to somehow avoid the paper bit altogether, but that's a ways off for now.
ETA: The whole bring the sheets to a club meeting and then mail thing is completely classic. That's how we used to do it, but it was a really long delay and blah...