It is also possible your gluten reaction is more sensitive than you think. My neuro symptoms are the only ones I noticeably have when I eat gluten, and they've gotten better if I avoid anything that will likely have traces. This mainly includes flours which are labelled gluten-free but will probably have some miniscule amount in them. Studies that show that less than 20ppm gluten is safe are based off of villous atrophy only, least the ones I've seen. Which makes sense given that the official diagnosis of celiac disease is based only on intestinal damage. But it doesn't make much sense given the extent that this auto-immune disease manifests itself.
That said, I've been gluten-free 10 months and I'm nowhere near healed fully. I've had celiac symptoms for 13 years now though (could very well be longer actually having it), and extensive intestinal damage, and of course, neurological symptoms such and tiredness, poor concentration, and perhipheral nerve pain.
There are more nutrients than just the previous ones listed that you might be deficient in, ones that could be responsible for nerve damage, such as vitamin E. Also be careful of what dose you take, B6 for instance could CAUSE nerve damage if taken in a dose even as low as 50mcg/day...granted that's probably if you're not deficient in it.
Nerves themselves don't repair quite as easily as many other body parts, (think parapalegic), but it's not impossible nor do motor neurons represent your entire nervous system. (I think it's only the myelin sheath that has problems regrowing, not the neurons themselves.) Grey matter by definition isn't myelinated. Even with extensive brain damage, a motivated person can regain many lost abilities, as the brain reroutes pathways.
Annd, as to how bad it can get...very,very bad. Be thankful you don't have any ataxia. At its worst, celiac disease can kill. If you are careful with what you ingest though, this isn't a worry in the least.
Gah, keep adding to this. The neuron symptoms are likely caused by your immune system attacking itself, much like the villous damage is by your own immune system. It is possible it is only a vitamin deficiency, and likely there's some vitamins you're deficient in regardless, but I'd play my bets on the damage being purely the celiac disease itself.
I found this article very insightful, and it was the hammer in the lid that made me realize my neuro issues were the disease itself, not just nutritional problems.