There is no reason to doubt your doctors, but obviously you need a different solution. First, the green-brown mucus usually indicates a sinus infection, although only a CT scan would say for sure. At any rate, a Sinus Flush would clear that out:
http://www.medhelp.org/user_journals/show/2322
The Flip-Turn Sinus Flush is mildly risky, because you have to bend over to do it, preferably in a shower, but you can also do it outside on soft ground.
You should see some results after 4 or 5 days of twice-a-day flushing. If not, stop, and even if it does work, stop after 2 weeks.
Next, scroll down to the comment section, to silkysoft on april 17, 2009. She had a problem like yours, and the reflux drugs were drying her throat, causing the thick mucus. Her doctor successfully prescribed Gaviscon Liquid, which was less drying.
Another cause of stringy thick mucus is new-fangled mouthwashes or toothpaste. You can figure that out.
Kjelltp may be very well be correct, but if so, look for a holistic doctor with a medical degree, or you could find yourself dealing with Unicorn Therapy. The models for these kind of doctors are Dr. Mark Hyman and Dr. Diana Schwarzbein, who you can google.
Insulin imbalances can cause mucus problems.
Lastly, in terms of systematic phlegm, Chinese medicine is very effective. You should be able to find a good D.O.M. in the Metroplex.
That's all I got. Good luck.