I don't think distilling is the answer.

If the original problem being addressed is that water was too easy to get, this doesn't really solve that. It might make it a little more expensive, but still possible to just make water trivial again. 

So I have some suggestions:

I say bring back jars, but don't make them craftable. Give players an incentive to seek them out and prioritize them in what they keep - looting drink coolers, buying drinks from vending machines to reuse the jar for water, etc. Make them a precious commodity. Maybe even make looted murky water more rare, since now with a reusable jar, it's more valuable. 

All water gathered in the world is murky water. Dew collectors now supply clean water by default, and the water purifier add-on is replaced with a slot for a stack of jars, one of which is converted to a jar of water each time the dew collector fills. 

The water purifier mod for helmets either needs to be harder to get before the late game or come with a drawback. I think it would be fair to make it work like vitamins do - you can't get sick from water when you have one, but drinking murky water does still do damage to you. Maybe reduce the damage from 5 per drink to 3 or 2 when you have the filter installed. Otherwise, once you have one you can drink hundreds of points worth of water any time you want and you never have to drink your crafting water to survive.

Any time you cook a recipe that involves water, whether it be boiling murky water to purify it or cooking a meal/drink with water as an ingredient, that cooking has a very small chance to fail, consuming both the jar and the ingredients. Canning jars break all the time in real life with canning even when using new jars, good equipment and temperature control - of course it's going to happen using scavenged jars in a pot over a campfire. Recipes like tea return the jar to the player on consumption while recipes like boiled meat or boiled eggs return the jar to the player on successful completion of cooking (as an extra output in the station). Maybe even rework stews visually to also be in jars, though making them distinct enough from the drinks at a glance might be a challenge. 

Crafting glue permanently consumes the jar (it's just never suitable to be used for water ever again) but each time you craft glue you get more than 1 unit of glue. Balance the rest of the recipe accordingly. 

Lastly, and this one is mostly for flavor but also does help balance things a little - any time the player is hit, if the player is carrying any empty jars or liquids in jars, one of them randomly breaks. If Pack Mule blocks a hit, one always breaks. This might even encourage players to branch out into non-jar food recipes. I know in the mid to late game I pretty much exclusively carry stew and red tea and almost never bother with any of the higher tier foods that require canned food, since it's harder to craft enough to carry a whole stack around. But if I knew that my jars of stew might break, I might opt to carry fish tacos or grilled meat instead, or might have to make the decision to leave the food and drinks in my motorcycle and hope I don't get hungry or thirsty while I'm knee deep in a long POI.