--as to whether "alcoholic neuropathy" is caused by the effect of alchohol on the nerves themselves, or whether the prime mechanism is nutritional deficiency; heavy drinkers tend to get certain vitamins/minerals leeched from them in the process of metabolizing alcohol, and if one does not have a great diet to begin with, or has some genetic difficulties in nutrient utilization (more common than most doctors think), one can get neuropathy from lack of vitamins (especially the B's) or mineral imbalances.

If nothing else, though, there are some reports of people with neuropathy thought to stem from alcohol arresting, or even reversing, the course somewhat if they stop drinking and systematically start dosing with large amounts of essential nutrients. Everyone is individual, and much may depend on the extent of the damage, but peripheral nerves can regenerate given the right conditions, though said regeneration may be patchy or incomplete.

I realize you don't have a lot of money for testing right now, but if you can get some done at some point, you should drive the protocol--nerve studies of your feet and legs should be done, which might include qualitative sensory testing--if you have primarily small fiber damage at this point, standard EMG/NCV testing won't reveal it. I think you're on the right track with supplementation--most of us recommend high doses of methylcobalamin B12, along with 25-50mg ranges of other B's (with perhaps a bit more thiamine and niacin), considerably more Vitamin D than "standard" ranges indicate (2000 IU and up daily for those who don't work in the sun), calcium/magnesium in roughly a 2:1 ratio (and not magnesium oxide, which is not appreciably absorbed by the body), and perhaps alpha lipoic/R-lipoic acid, Acetyl-l-carnitine, coenzyme Q10 (this last one is particularly important for mitochondrial problems--and many heavy drinkers show mitochondrial damage). This can get expensive, we know--so often some one-at-a-time experimentation is in order for these.

I would hope at some point you can get a complete work-up (including vitamin/mineral measures) at a competent neurology practice that specialize in neuropathy (not all neuros are very well versed in it).