Contact the ranger office and ask what the recommended water treatment procedures are for the backcountry. It sounds like you're developing a very complex procedure (that requires you to carry around a whole bunch of water) to save a few bucks. How much are you saving when you add up the cost of the water containers, the brita filter, and all of the extra fuel compared to a Sawyer mini at $25 http://www.rei.com/product/866577 ( and less than $20 at places that don't carry the REI guarentee)?

There are also chemical treatments that can be pretty cheap.