It's not surprising you didn't do well on Effexor -- it's a very stimulating antidepressant and not usually used when anxiety is the primary problem. The ssri class or tricyclics would usually be used for anxiety as the primary problem, so I have to say, added to your psychiatrist saying she won't help with your taper, I'd find a different psychiatrist -- one killed me, so be careful with them. Especially if they take insurance. So your negative reaction to Effexor is the usual one for an anxiety sufferer -- it targets norepinephrine, basically adrenalin, as well as serotonin, and so is very stimulating to most people. Also, along with Paxil, the hardest of all these meds to stop taking. Not the place to start. Usually they start with Prozac, which, while stimulating, is the easiest to stop taking, and then Lexapro, as these are the two with the supposed best profiles for least problems. Zoloft probably works for the most people on this site. I was started on a tricyclic, imipramine. My psychiatrist, who doesn't take insurance, doesn't use the snris, the class Effexor is in, for anxiety sufferers. As for L-theanine, when I managed health foods stores I never met anyone it worked for, including me, and I'm not sure anyone knows exactly how it works in the body -- it's an ingredient in green tea. But I don't think it would hurt, I just don't think it will help by itself. With herbs, combinations work best. The best systemic relaxant is said to be passionflower, but again, it works on GABA at least in part. I have heard of The Road Back, but have never tried it. As for tapering, if you have to do it yourself because you like this psychiatrist, just do it slowly. You've only been on it a short time, so it shouldn't be a problem. Try a book called The Anti-Depressant Solution for discussion of tapering off drugs.
Worth noting that we are also checking for any viruses that could be a culprit. She also checked thyroid, iron levels, and B vitamin levels. All looked good.
I should add, you can always try homeopathic remedies along with drugs as they don't contain active ingredients, but they're also pretty hit or miss.
Basically, the standard warning is not to take kava or valerian when taking a benzo, as they all target GABA. The drug is obviously stronger than the herbs, and kava is stronger than valerian as a relaxant. GABA supplements don't usually pass the blood/brain barrier, so they not only shouldn't be taken along with a drug targeting GABA but probably won't work. Now, many people are prescribed gabapentin or Lyrica while taking a benzo, and those are basically GABA shot right to the brain, bypassing the digestive system. And if you time it right, given how quickly benzos wear off, you could, if you really knew yourself and how your body reacts and really were expert on the use of herbs, you might be able to supplement the drug with natural relaxants, but again, it can be dangerous. Most practitioners of natural medicine don't really think it works that well if you're taking pharmaceuticals, particularly if you're targeting the same part of the body. If you decide you want to pursue the natural route, be careful stopping the Lorazepam -- if you're taking it every day it is an addictive drug and will become harder and harder to quit the longer you take it that way, so it has to be tapered off of at a speed that suits you. On the other hand, you don't say how you collapsed at work or why -- GAD and Panic Disorder build up usually before they become chronic problems, and if they're not chronic you usually, or should, be sent to a therapist, not given a drug. Physiological causes should also be looked for -- for example, I don't really know what adrenal exhaustion is, but the adrenals are intimately connected to the thyroid, and thyroid problems mimic mental disorders. So do blood sugar, other hormonal problem, etc. I don't think you're having tolerance withdrawals -- those happen when you've been on a drug a long time and it stops working. What's happening to you is, benzos, particularly the one you're taking, don't last that long in effect and they're wearing off. When they do they can also leave you tired. Antidepressants, when they work, work all the time, they don't wear off the way benzos do, but then you're on an antidepressant and they're hard to stop taking, too. There are herbs you can take to help the adrenals while you're on benzos or antidepressants, as they don't target the same neurotransmitters -- two examples that are relaxing are ashwagandha and holy basil. Eleuthero is useful as well but can be invigorating. I'd recommend a book by Hyla Cass, an academic psychiatrist, called Natural Highs for the natural approach overview. Usually you would use substances, mostly amino acids and relaxants and adrenal support, in combination, along with therapy, exercise, meditation, dietary changes, etc. A holistic approach. No approach comes with guarantees of success. Good luck.