Over the hump...

I think that there are a lot of variables at play, why were you a mid level team before dictates what you do to get them over the hump. There is more than one way to skin a cat and there are many reasons why teams fail to succeed

Was at a school once that won a title once about a decade ago with what I was told was a stellar class of athletes- but other than that bounced around .500 since. They had no offseason or summer weight program to speak of, didn't watch films, but did a lot of team bonding events. Upper middle class kids for the most part who were used to this system because thats what was done for the one title year so thats what always had been done. Kids were used to this, and accepted this as the way things were.
So, the things we did addressed those issues we saw needed adjustment.

Conversely, I once was at a school that was in an economically depressed area where kids were dealing with gangs, homelessness, and a number of them were raising kids of siblings themselves. The issues were different and we dealt with them differently.

This is a good point.

You also don't see them with just average offensive lines

I really think this depends on what the hump is. One school where we took over that jump was posting a winning record for the first time in well over a decade and a playoff berth.

Program I'm in right now, it was making it beyond the state semi-finals.

Another school the hump would have been going .500.

Once you have won district 2 years in a row and can't get past the 3rd round of the playoffs, then what?

One team in our area went from maybe 1-9 in 2014 to 9-1 in the first ten games of 2016.  They honestly didn't get that much better athletically, just MUCH MORE disciplined.  (To be fair, I think the competition went down a bit, but not THAT bad).  They went to option.  And I think bigger than the fact that they went to option is that they run maybe 5 total run plays: Midline, inside veer, toss, belly/counter lead (same play, just one has counter action), and maybe a few times a counter trey.  They paired a couple play action passes with this.  And I think a rollout for 3rd and long situations.  To me, it seems the way to go.  Simplify.  In their offense, each lineman does only a few different blocks based on the play.  It's easy to get good at what you're doing when you are only doing a few different things and don't have to think a whole lot.  

One thing I'll say is that I like the OL having a niche even if it means you can't run some of the stuff you'd like to.  Think about a Wing-T, which on paper I think looks awesome.  But your guards have to be able to trap inside, trap outside, rip to the second level, baseblock a DT (who may be quite a bit bigger since you are wanting the guard to be agile enough to pull so much), pull lead on buck sweep, etc. etc.  In this triple option it's pretty much block the guy over you or take a good angle to the second level.  Now, there are finer points to it, obviously, based on alignments, but each block can be condensed down to a very simple thing and can be repped a million times since there's only a few categories to work.  

I also think the Option choice worked out because the defense wasn't the greatest thing in the world for them, but because they did what your typical option team does, they got some of the same reactions from opposing offenses.  They hold the ball for a very long time and then put up points, so the opposing offense feels they have to press a bit more and as the game goes on every time they manage to get stop and then make a long drive for a score, the opposing offense gets more and more predictable, which obviously helps their defense.  

Outside of that, I'd say the biggest thing is to be very good about how you use your best athletes.  You've gotta get that right.  And to do that, you have to decide what you want to do.  So, I've seen it happen where a guy is saying "we're going to RUN THE BALL flat out!!"  But then look at a player and think wow, he'd be a threat for people to worry about on pass at this or that position.  Not saying if you're running the ball you don't want to have passing threats, but to me if I've made up my mind we are going to be good at running the ball, and we're going to spend the vast majority of our time being good at it, the guy that I think is a matchup problem or ANYBODY on their defense is going to be in the backfield and I'm going to be feeding him the ball.  That's just my way of looking at it.       

On defense, something I've grown accustomed to saying recently (stole it from someone, haha) is that we are going to do the easy things better than everyone else.  My thought process is that a large number of the things that you have to do to be successful at doing your job on defense has nothing to do with how strong or fast or athletic you are.  Think about it like this.  I can't count how many times I've seen a DE get upfield when unblocked and get kicked out by a guard who didn't take a great angle for the kickout.  If the guy had pinched hard inside and wrongarmed that guard, the ball would have been forced to bounce out to an unblocked defender.  Doesn't matter what the two guys bench press or 40 times, if that DE had taken advantage of the fact that the guard hadn't taken a great angle to the kickout and put himself inside that guard, then things would have been much better for us.  

As mentioned by several folks already, there's no magic bean.  I think the first thing your have to identify is what exactly is the cultural makeup of the school community and what are the issues that the school has to deal with or address.  I've been in a couple of these types of situations - trying to move a program from mediocre to something more.  Both were very different situations.  One of the common things in both was trying to create an identity, something unique for the kids to latch on to.  Another was creating a standard for what is going to be accepted and not budging from that standard.  It doesn't mean you have to be a ruthless dictator, but enforcing the rules you have consistently.  

The school I am at now had been over the hump.  There were multiple state championships won here and it was considered a contender every year.  There was a coaching change and things slipped back into the range of mediocrity.  One example of a simple standard change was practice and weather.  The coach before us -- if it rained practice was cancelled and everybody goes home.  We just simply said if the weather makes it so that we can't be outside, we will be doing something, somewhere; no matter what -- film, gym, quick workout, chalk talk, etc..

We came in and made the theme for the year No Days Off.  We gave the offense a slick name, the WR coach gave his position group a slick name and put up some posters, gave the defense a slick name.  Started out 5-0 finished 6-6.  So the next year we made the theme FINISH.  And so the story goes.  

There was talent here.  There was community support and admin support.  One of the biggest changes was the HC changed the S&C coach.  Even though we have 'gotten over the hump" we still have to hammer these kids everyday about the fact that we have set the standard and we are not going to accept anything less than the standard, for what every the expectation maybe.  We play in a very competitive league (4 of the 5 teams have won multiple state titles about 36 total), so the difference between 1st place and 5th place is very little.  We constantly have to harp on the little things.  It gets tedious and down right monotonous.

The other stop was similar and yet different. A very socio-economically disadvantaged area.  There had been some success and talent there, not state titles but one appearance and several conference titles.  But there just wasn't much in terms of being able to all the resources you want/need.  It wasn't a school that many coaches would point to and say, "I want to go coach there".  The HC was able to have a bit of a perfect storm and put together a really good staff of local ACs; we all either played there or from nearby schools.  We tried to give the kids an identity and something they could be proud of.  And often times it wasn't much -- a special sticker on the helmet, shoe spats for the playoffs, a unique/different pregame warm up, running a few trick plays, etc....  And we had a few hard and fast rules and stuck to them -- things like if you don't come to practice, you don't play, etc...