This is where a filter, even with a prefilter, will clog every time, as Phat tells us. I'd do the filtering through the bandanna bit, maybe several times through several thicknesses. Letting the dirt settle out does work, but takes several hours, which you didn't have.

Katadyn Micropur tablets are chlorine dioxide. They are also EPA approved, unlike Aqua Mira. (Although Aqua Mira's tablets, I'm told, are made in the same factory in Spain as the Katadyn so are probably identical--pick whichever one is cheaper.) I carry enough chlorine dioxide tablets so that if my filter breaks or mud happens, I can use them rather than having to abort the trip. I hate using chemicals (after a horrible experience with iodine) so normally rely on the filter.

However, make sure you use one tablet per one full quart of water. No wonder the water tasted awful if you used one tablet for only half a quart! The liquid mud, of course, slows down the action of the tablets as well as possibly not being good for your insides. The more you can filter out with the trusty bandanna, the better.

A better possibility, since you were already short of water and couldn't wait for the chlorine dioxide to do all its work, would have been first to use the bandanna and then to boil the water. Since you were cutting the trip short, you didn't have to worry about running out of fuel. Boiled water tastes awful, too, but once you aerate it by pouring it back and forth between two containers a couple of times, it tastes fine. The one time I encountered a similar situation, we bandannaed and boiled.

These sorts of experiences are how you learn! Theory can go only so far.