Respectfully, I have to disagree. Removing wood barrels is difficulty for difficulty's sake. Might I suggest the rut is the nerfing of items and the removal of recipes rather than creative thinking in terms of quests and outcomes.
I can grow a tree, I can harvest it, I can build a few dozen different tools and other blocks from it, including a wooden frying pan(?!?) but I can't craft a barrel? Really?
You most likely will not be able to preclude rain. Nekoali suggested making rain water be salty. I'm not certain if you can change that game mechanic or not, but it would be a much better route. It makes sense internally to the story.
Given salt water, I can boil it, collect the steam, condense it and have potable water. And salt, by the way. It's a fairly basic survival skill. Given the amount and infrequency of rain, it is hardly an infinite water source. Indeed, not being prepared for rain would very likely be fatal, given our storyline.
I don't mean to be overly argumentative, but your zeal to limit water is to me, at least, overly obsessive .
Change water in a wooden barrel to salt water, and permit that salt water to be transformed, at a cost, to potable water, and you have more or less defeated 'infinite water' is a measured, reasonable way in the early game. By mid-game, if the player can't produce water pretty much on demand...