Kevin's right about flocculation. And people have had good ideas about carbon. I deal with this at home (middle of a spruce forest) and on toxic waste sites (my day job) and while rafting.
Granular Activated Carbon (GAC) can remove tannins (both the color and the test) from drinking water. The Brita filter in the Brita pitcher does fine at my house, although I hate the price per pound in those little cartridges - when I buy GAC by the thousand pounds, it's $2-3/pound.
I use a lot of GAC vessels, have designed a few, and more often tweak other designs to do what I want. You need a certain contact time and anything that moves the water quickly past the GAC isn't going to acheive high removal efficiency. This makes it not so great for a pumping/sucking scheme because you want that to happen quickly. But it makes GAC ideal for a gravity-fed system because they you care much less how long it takes. Make your carbon container long to maximize contact time and relatively narrow to minimize weight and volume. For 2 people x 10 days, you'd need so little GAC, 1 cm ID by 10-15 cm length would more than do it. Syringe bodies would be one off-the-shelf item of that size and the tips could fit nicely into your tubing (maybe drill out the inside of that tip for better flow and strap two together back-to-back to get those "hose adaptors" on each end. But you could also look for a plastic filter housing with room for a cubic inch of GAC and use fine screen or coarse filter paper to hold in the GAC.
Then play with it - a high head will move more water and maybe that's fine, but if you still see color or taste, use less height in your gravity-flow system for a lower flow and longer contact time.
But the real UL method is bring some alum. It's in the baking or spice aisle at the grocery store, is food grade and really speed up clays and silts settling from the water (think Colorado River water). Just add a pitch to the water in your biggest pot, come back in 15-30 minutes and sediment will have gone to the bottom and they'll be a floating scum layer that was the dissolved tannins. Decant the clear water off gently, and/or use a scrap of (unused!) toilet paper or coffee filter to wipe the scum off the surface/edges of the pot. (Mostly, it adheres to the edges of the pot, and you can eliminate 95% of it by just pouring it gently into other containers. 10-20 grams would last you two weeks - finding a SUL container for it will be most of a weight!
Now, whatever purification you are using - UV, halogens, physical filtration - has less to deal with. UV travels further in clear water. Chlorine and Iodine aren't used up on tannins and sediments. Your filter won't clog up as soon. And some bacteria, cysts, and viruses will have settled or flocc'ed out - potentially a large fraction (90-99%) of them, but I'd still treat with something, but I worry much less about the amount and time of UV or CL/I if the turbidity has so dramatically improved.