The white spiral shaped specs that you see in your tank are called spirorbid worms. They can extend the tiniest of featherduster-like feeding tentacles.

Do NOT use a Brita water pitcher for your tank water. Last I read, it uses silver as part of the filtration system. You don't want metals in the water.

If you get an RO/DI unit, hook it up downstairs. Get yourself some 5g jugs from your LFS (Local Fish Store) and lug them upstairs as needed. It won't be comfortable, but it is that or some interesting plumbing perhaps.