I have been thinking a lot about my pancreas and liver lately - also recently discovered I have RH.
I'm not sure if you were looking for some explanations for what may be going on in your body, but it seemed like you might be wondering.
I think the "story" of what is happening to you is that you are very insulin resistant. This is why you spike so high (even with such a small number of carbs). Your pancreas is still making insulin, though, and keeps upping its amount to bring down the blood sugar until finally the cells start responding. But at this point, excess insulin is in your bloodstream and causes your blood sugar to eventually dip quite low. We call it "reactive" hypoglycemia because it is an overreaction of your body to carbohydrates.
I would suspect that carbs (even relatively small amounts) from your dinner could explain the hypos during the night. I know it doesn't seem fair that you have such a big reaction to a low carb meal.
Your symptoms of neuropathy are discouraging, but probably mean that whatever your spikes have been going up to, they surpass your body's personal tolerance for keeping healthy nerves! Sadly, some of us get these complications at lower levels than others.
The best discussion I have found (in my limited research so far) is the book Sugar Nation by Jeff OConnell. He devotes several chapters to it and really gets into the possible physiology of it and the various types that exist.
Headaches are associated with RH most assuredly. From tracking my own episodes (I wear a CGM now), I can see that I get a headache right at the peak of the sugar spike (BEFORE the low, although the headache REMAINS during the low and even after recovery). I am starting to suspect that the massive insulin release might actually trigger the headache!
Dry mouth upon awaking could very well reflect the surge of epinephrine that your body releases in order to bring your blood sugar up after a hypo during the night.
If, right now, you can't seem to tolerate carbs - don't eat them right now. See if you can find some stability without them for awhile. "Eat to the meter" as we say. Find the foods that don't spike you OR lead you to a hypo.
You can do this! You are the experiment.
Also, although I understand that the nifedipine is meant to reduce your overall sympathetic response and possibly help reduce hypoglycemia, calcium channel blockers are renowned for their many side effects - it alone might explain some of your bad symptoms. Additionally, I hope it is not causing you low blood pressure which would be making you feel horrible. Do you have a home battery-operated blood pressure meter? You can get them on Amazon for super cheap to make sure you are not experiencing low blood pressure episodes from the doubling of this medication.
Good luck. Please report back as you learn more.