With enough patience, ammo, and firecrackers, you too can get into the top 50 players for state of decay breakdown. I made it to #1, but am now #3, using this strategy. I got so bored at 280,000 points that I just didn't feel like doing something just to have a great score any more. But I'm easily bored... so maybe you'll go even longer. I also had a bug where no more missions were spawning, so I had NOTHING to break up the monotony of this easy strategy.
All that being said... here's how you do it in a picture:
Notice all the cars? Yeah this obviously isn't a breakdown game. Just some random screenshot I found googling map of marshall. The red dots are explosive propane tanks, the green dots are bushes for you to hide in, and the black line is a suggestion for how to drive in between the two locations.
All you have to do is pull up to the tank (don't park too close!!!) and throw a firecracker to the right or left of it. Don't place the firecracker right on the tank or you might have trouble hitting it later. Now, go hide in the bushes that I marked on the map and crouch. Once a sizeable force is on top of the tank, stand up and shoot the gas canister. KABOOM! You'll get anywhere from 250-700 points depending on how many freaks are involved.
Once you wipe the goo off your face and weapon, jump into your car and drive to the next canister. Repeat this process going back and forth until you run out of firecrackers.
To prepare for this strategy, I created 560 firecrackers (2 stacks). After revealing this method on the forums, I noticed that four new people magically appeared in the top ten for breakdown's leaderboard within one week. Usually we'll see one in like a month break through to the top ten, but this was four new faces in the same week! Coincidence? I think not.
Obviously this method requires that you spend some time, possibly several levels, stockpiling ammunition on your characters by breaking open ammo boxes as well as turning the rest into firecrackers. My favorite method is to build four workshops and a medical facility at snyders, then just pump out firecrackers as quickly as I can find ammunition. 4x3 = 12 firecrackers every 5 minutes x 12 = 144 firecrackers per hour.
The other half of this strategy is going for infinite resources. I would use that post as well as my ideas on sleep deprivation to create a long lasting survival method that will give you enough time to build up points for a high score before your survivors start starving to death.