Your solution might work, but in general "dadamit" specifies a goal, whereas "because" specifies a cause.
Still not sure how to translate it best.
[...] so that it won't fall into the water.
[...] for it not to fall into the water.

"so that" works perfectly. Thanks.

Leo bietet noch 'lest' für 'auf dass', 'damit'.

FWIW, I want to use "limb" for this. Only limbs are heavy enough to influence which way a tree falls down.

My 21st century suggestion:
Of course we need to be sure to choose just the right tree which doesn't have its heaviest limbs towards the water side, so that it won't fall into the water during felling.

Thanks opine & manni3. "Lest" might even be better given the age of the source. I'll consider "limbs," but so far I've been trying to keep as much of the rhetorical style of the age of the source in mind. But I'll consider it.

"but so far I've been trying to keep as much of the rhetorical style of the age of the source in mind" -- OMG, I'm even writing like it!