Question : Do you really want to see a score that's almost better than your's and a half ?
Of course. I would immediately realize that I'm missing something/doing something wrong.
Second question : What does it matter when I post my highest score ? I play the game for two weeks to get the highest score possible. For me it doesn't matter if you post the highest score one week into the competition or at the last second. If my score is better than the rest, fine. If not, also fine.
If I were playing just to beat everyone else by a hair, I'd have to accept that it might backfire. Sooner or later someone would hold back a better score until the last moment and then I'd be screwed.
Deliberately under-performing is just bad sportsmanship in my opinion. Now this obviously can't be enforced, but I will always post a new high score as soon as I get it.
Guess I'm going for 3rd, since I don't know the secret knock.
The secret is to stand just the right distance from the playfield border to always make the big ape spawn right in front of you so you can punch him right as he appears and before he has a chance to attack you. At least that is my strategy, dunno if yam found something else.
I position myself so that the tip of the kangaroo's foot is in the middle of the left bar of the ladder. Then you just spam punch. When done correctly you can hit the monkeys climbing up the tree at the same time.

Only thing to watch out for is the apples from the top and occasionally a monkey might throw an apple from the side, but they generally don't while the big ape is in the lane. You can get like 40-50k on your first life in the first level. Works in the second level too.