I know this is old now, but I wanted to update it with something that might be valuable to other people.
First of all, I have since stopped using activated carbon in all of my tanks, paros and otherwise. It’s too difficult to find a brand that actually will not raise pH and sponge filtration seems to be working better all around anyway.
Second, the rainwater was dirty for a few reasons. We had a very dry and hot summer, which meant that more debris and air pollution ended up sticking to the roof, and then the rain washed it down; I have since found that keeping the roof clean (or at least keeping the surfaces and gutters that contribute to one’s collection apparatus clean) by simply rinsing them with tap water from a garden hose (i.e. standing on the roof and spraying it down) goes a long way towards keep the collected water clean. I usually wait to set up the collection apparatus until the rain has had a chance to rinse away any minerals from the tap, but this does not take long under sustained moderate to heavy rainfall.