Joe, that is a good question. Here is my take on it.
I think post-season success is only one factor of marketing a wrestling program. I'm not the coach at a small school, so of course all my ideas are from "theory" only. I realize you are out there working in the real world as a small program coach, and you may legitimately say that these ideas are good in theory, but not practical.
Here's just some ideas off the top of my head how I would approach it:
1. DEFINITELY begin with the youth/feeder program. The best way to ensure a strong high school program is to shore up the feeder program. Having some little kids myself, I can tell you that at the elementary age, they have absolutely no concept of whether or not the high school program is qualifying kids for state, or whether or not the team is advancing out of sectionals. I would work with the other local youth athletics (football, soccer, baseball, even basketball) and build a good relationship with those coaches/league directors. Ask them to encourage kids to come out and try wrestling. They know the kids, the kids usually trust them. They can be a huge ally for steering more kids to give wrestling a shot.
For the youth wrestlers, I would have several clinics that are free for any kids to come out and try wrestling. I think many parents would be willing to take the kids to try it out if there wasn't an immediate upfront financial commitment like many of the youth clubs seem to be (you have to join USA wrestling and the local club) Make the clinics a lot of fun, mixing in wrestling-related games while you are showing the kids a few moves. I think that the majority of 2nd-5th grade kids LOVE the idea of having the knowledge to grab another kid and be able to wrestle them to the ground. I would personally not make these free clinics overly-technical. But I might have a couple of your skilled high school wrestlers to come in and do some live wrestling (and they better be VERY active) while you explain briefly how points are scored, what are the three periods, etc. Can you get some time in the local elementary school PE classes to have a couple of wrestlers come with you and give a demo, then show all the PE kids how to do a double leg and a half nelson to pin someone?
Do some creative promotions to get the kids to come out and watch the high school matches. You can pick up little marketing gimmicks online (oriental trading company) in bulk prices for next to nothing. Make up some tie-dye tshirts and throw them out into the audience. Anything to get people to talk about it the next day at school and come back for more. What do high school kids want -- somewhere they can go for cheap, hang out with friends, and act like a fool. Look at how many college basketball programs have attracted a rowdy student section -- they have a designated section like the Paint Crew (Purdue) or the Cameron Crazies (Duke). Buy them some hair paint, again have t-shirts made up, give them something "cool" to be a part of. Can you think of any way to have a "halftime" or some break in the action, and invite elementary kids to come down on the mat and do something (not sure what) -- like they let kids shoot freethrows at halftime of basketball?
Have one match a year (preferably one that you are pretty sure your team will win) where you have a "pack the house" night. Reduced or free tickets or let them in free if they bring a can of food for a local food pantry. Offer that your assistant coach will shave his head if the team wins by a set amount of points, heck let some elementary kids take clippers and buzz the hair right there in the gym. If you can dim the lights in the gym and put a single lamp down over the mat (similar to the state finals), do it -- that is a cool environment. There's got to be some kids out there that will see one of the kids on your team score a pin, hear the crowd hopefully go WILD for him, see his hand raised, and think to himself "woah, I want to be a part of that!"
Again, just throwing out some random ideas