The problem of access and finding Persons of Peace

Two of our kids have been involved in a community football program this year, and with football comes a bit of fundraising. The mechanism of choice for this community program is door-to-door raffle ticket sales. They did pretty good, but it was very enlightening, and there are some lessons that ministry needs to consider.
When they started the process, the program basically said it was mostly a matter of perseverance in going house-to-house: so many doors knocked on, so many open, so many requests made, so many buy tickets. If you knock on _x_ doors, you’ll get _x_ sales based on this formula.
The problem we encountered: depending on neighborhood, just because you knocked on _x_ doors didn’t mean _x1_ doors would ‘open.’ For those who came to the door, the kids did pretty good with the raffle sales. But a lot of people didn’t come to the door. Maybe they weren’t home. Maybe they were, and just chose to ignore. Whatever the case might be, the net result was the same.
This is an important point: urban cultures (at least in the USA–someone chime in for other cultures?) have gotten very good at walling ourselves off from interruption by others. We don’t visit our neighbors, we fast-forward past advertisements, we don’t pick up the phone if it’s a phone number we don’t know, we say “I’m not interested” and close the door in peoples’ face (yes, that happened to our kids). Essentially we are shutting ourselves off from any contact outside our immediate social network.
So, perhaps the solution is to use our social network and word-of-mouth referrals? The challenge: globally 86% of all non-Christians don’t know a believer. Believers and non-believers don’t share social networks. This number is lower in some mostly-Christian areas, but in those places, non-believers can be divided into two camps: historically non-believers (e.g. migrants, diasporas, etc.) who are culturally cut off from Christians; or, post-Christians who are disinterested.
Is there a solution? There’s not an easy one. It’s one of the reasons why short-term trips and short-term efforts fall short, as do periodic advertising campaigns–because people throw out the ads, the cards, the tracts, and don’t open the door. One way to start on a solution is to make a special effort to get to know neighbors, and to prayerwalk the neighborhood.
(And note, this “blocking” isn’t necessarily an attempt to block out Christianity. It’s rather a larger walling off that our culture is doing–we stay behind our fences, in our air-conditioned homes, with little contact with neighbors. This may be an urban phenomenon: has anyone done studies of rural vs. urban in this regard?)