I'll tell you what I think... but this is not a diagnosis by any means...

Antibiotics work by affecting either the cell wall of the infectious organism, so it dies, or by attacking the DNA of the organism.
With time they will do this to you too.

If your dorsal root ganglia along the spine are damaged by the Lyme process or the drugs, that is a serious thing. Some people lack the genes to make the nerve growth factors to repair this.

There is a special MRI test that will show dorsal root damage. Have you had it?

This is the link to that thread:
http://neurotalk.psychcentral.com/thread147771.html

The fact that gabapentin works for you, hints at this because that is the level that this drug often works at.

Supplements to target mitochondrial damage are acetyl carnitine,
lipoic acid, and CoQ-10. Ribose powder (a sugar) also may help
with normalizing ATP production in the mitochondria.
Magnesium is important too, as it functions at the mitochondrial membrane.

I have these supplements in the supplement thread:
http://neurotalk.psychcentral.com/thread121683.html

If you haven't read the mito threads yet, I'd search them
"mitochondria" because this is where the damage can occur to nerves.

In your case things are really complex. Could be that a bunch of factors co-exist given your Lyme infection which impacts nerves, and the antibiotics which also carry their own risks with long term use.

For symptom relief of your feet, have you tried Biofreeze gel?
This really works for me and some other posters here too. The gel carries the menthol thru the skin quickly, and the menthol then stimulates cold receptors to override perception of the heat sensors which seem to be the most affected by PN.
Biofreeze is now available at low prices on Amazon, and iherb.
I've used it for years now when my feet flare up at night. It never fails me. I think it is worth a try... as it is under 10 dollars.
A little goes a long way. I learned this trick from physical therapy I had several years ago for a tendon injury. My therapist mixed Biofreeze 1/2 and 1/2 with the ultrasound lubricant for my Ultrasound treatments, which they ramped up in power.