I suggest you try using multiple small extraction volumes instead of a single big one. The long extraction time could be shortened, and you will get less heavy molecules out (which in tea, for example, tend to make the brew taste a bit bad). See [1] for an explanation. It might just taste better, let me know if you try it!
[1]: http://chemistry.stackexchange.com/questions/37712/why-using...
But here's what I did:
Get a big french press, a narrow mouth pitcher or a wide mouth bottle, and one of those single serving coffee maker funnels (mines a Hario, which seems to clog up more slowly).
Put about 3/4" of coarse coffee grounds into the french press. Fill it with water to a little below where the plunger sits, stir it a little, put the lid on (plunger up) and push it back under a cabinet on your counter where nobody will mess with it.
24-36 hours later, push down the plunger slower than you've ever thought you could push down a plunger. Put an unbleached paper filter in your single serving coffee funnel, put the funnel on top of your pitcher/jar, and pour. There's gonna be a lot of fines in the coffee so this may take a while. After you're done put the pitcher in the fridge.
Some people make a second pitcher from the grounds. It takes a bit longer to reach full strength the second time, so let it go for another 12 hours. But if you need the second pitcher before the first is gone your doctor may have some harsh words for you.