Yes I've cured my acid problem, but it was with more than just an alkaline diet. I've been very careful. I've been poaching any chicken or fish I eat to eliminate additional fats. I haven't added butter to anything. I found that avoiding anything fried or fatty has been the key. I just started adding almond milk (make my own) to my diet and it's working nicely. I'm slowly trying to reintroduce some kind of fats back into my diet...I need to put on a few pounds. I also noticed throughout this whole thing that Candida was indeed a huge factor for me. So I've been avoiding things like starchy potatoes and even sweet potatoes. I had a little sweet potato a week ago and it caused a bit of a acid flare up, which surprised me. But after a couple of days of being careful and drinking lots of water, my stomach was ok again. I've even been waking up lying on my back without any acid taste in my mouth! And the biggest surprise...my anxiety level is almost nonexistent now. It never occured to me that it was mainly caused by freaking out over the acid stomach. But now that everything is calm, the anxiety is out of a job.
If I were you I'd try the alkaline diet and my method of eliminating fried or fatty foods for a week or so before stopping your meds. Then wean off them to see how it goes. I don't believe in jumping from one frying pan into another when you don't have to. Give your body a chance to adjust to the alkaline diet first and then cut back to see how it works for you. Baby steps.
As far as sleeping goes. Even tho I found it really uncomfortable the first while, I slept on my left side and found it made a tremendous difference in how I felt when I woke up. The sleep will come as your stomach settles down and your anxiety decreases accordingly. It will work for you, but be patient. Just one task at a time. Initially I could barely think past my current meal and kept myself distracted doing things in between meals. As you improve, you'll find that it's less stressful thinking ahead a little. Now I'm even thinking about Christmas without feeling anxious about it.
And make sure you're drinking LOTS of water. I found that sometimes in between meals when I could feel the dry burn in the throat starting, I'd just drink some warm water (with a little sea salt in it) and it seemed to calm down the sensation. I keep a thermos of warm water next to my bed so if I wake up and my mouth feels dry, I just open it up and take a couple of gulps and it does the trick. Saves me from having to run down to the kitchen in the middle of the night.
Have you checked your pH yet?