I have Sjogren's (and several other things), and it is the basis of my neuropathy (both autonomic and peripheral/SFN) due to attack on the dorsal root ganglia.

It's a bit unusual that an eye doctor (I'll assume he's an ophthalmologist) Dx'd the Sjogren's with just a Schirmer test. It is quite common (up to 40%) for patients to be sero-negative for Sjogren's antibodies, but then a lip biopsy is usually done to confirm the diagnosis. There is SO many causes of dry eye/mouth, which the most common being medications. I'm glad your eye doctor is addressing this, but a rheumy (which you need to see as well) may not treat with Plaquenil (first line treatment for Sjogren's) without first having confirmation by lip biopsy. Sjogren's is a systemic condition, so you should see a rheumatologist for complete treatment (not just eyes). Since you have other significant conditions, this is even more important that you discuss with both your rheumy and neuro.

Your neuro may feel that your SFN is from the Sjogren's (if he agrees with the Dx). Then other treatment options (like IVIG or immunosuppression) may be considered.

There are Biotene products for dry mouth that are available OTC. Be careful with the humidifier, as they required constant thorough cleaning when used regularly due to mold build up very quickly.