I will offer one or two thoughts to this discussion.
Competition shooters are a small percentage of a larger group of recreational shooters that have become interested in such things as rifle tuning and reloading. If you want to increase the number of shooters that compete, I think that efforts to interest shooters that primarily shoot unmodified rifles, and factory ammunition in the next step up should be considered. I know that this is a long ways from inviting someone from a match, but to grow a plant, you need to water the roots.
The problem is that competition shooters generally already have maxed out their usage of recreational time on all of the various activities related to competing, and therefore do not have the time to do the necessary root watering.
There is also the problem of interest. If you are working as close as you can get to the leading edge of your sport, spending a lot of time helping someone take baby steps may be a bit boring, particularly if they are not strongly attracted to dealing with all of the little details involved in the more advanced areas of the sport.
IMO the thing that had the greatest influence in creating my interest in the more technical aspects of shooting was the writing, books and magazines. At the time, we did not have the internet, so the magazine racks and libraries were the only source of information. Today, I think that many have lost, or never developed much of a reading habit, except for the internet, and unlike the magazine rack that showed a variety of magazines to the casual passer by, if someone does not go looking for something on the internet, he may remain unaware that it exists.
So where does this leave us? I think that taking friends to the range, and making sure that they have a good time, so that they want to do it again is a good start. Beyond that, helping shooters that seem to be likely candidates for a more sophisticated approach to the sport would be next on the list. Somewhere in there would be finding a way to support one or more of the various junior shooter programs.
Like every other human, I always look for a quick fix, but some things require a more long term approach.
Back in the day, I got involved in helping to run a rifle and pistol club, not because it was always so much fun, but because I knew that having the right to have firearms did not mean nearly as much if there was no place to shoot them, and that for the long term survival of the things that I value and enjoy, young people would need a place to have the kind of experiences that I was lucky enough to have had in my youth.