My record so far is 6.9 meters. I found the following strategy to work well:
Since the farmer's approval rating increases with maximum height, rapidly growing vertically (and strengthening stems) while producing little to no fruit helps early on. When I reach 6 or so meters, with mostly leaves and little to no fruit to use up energy, I start branching out the very bottom of the plant to add tomatoes. Past this point, it's a game of trying to balance the plant as much as possible, adding fruit to to counter act the balance. When the plant swings from one side to the other, I'll try to add a branch just to go over the max height and gain more approval. With a strong stem, breaking the plant becomes pretty much a non-issue, but the weaker top can break off.
It's really fun! Spent a few more hours just now playing the game.
