Hi DCR! Still haven't met you, but found out that I did see you once when you attended a previous meeting. (I was at the springs but not "in" on the meeting, although I did overhear some of the discussion)
I think that putting out papers in any kind of box would end up adding to trash and providing kindling for those unwanted fires. Too bad, because it is an otherwise good idea. This is why I've asked about distribution, because I'd hate to end up just creating more problems for the springs I'm trying to help.
One approach might be to offer the flyer verbally and to ask the recipient to take it only if they will pack it out, or to allow people to read the flyer but not take it, or to have the points read off aloud if people want to listen. I'm not sure what is best. A sign, as Paul suggested about toilet etiquette, seems about the best, with flyers distributed at Bowen Ranch and maybe at the springs to people who agree to pack them out. If group members bring some flyers with them each visit and distribute them carefully, we may avoid adding to the trash problem. I would like to see other suggestions on distribution.