I take both Neurontin & Norco (hydrocodone w/less of the APAP). The Neurontin deffinitely takes some time to really build to a steady level in your system, and this is why they titrate us up. As you know, different people tolerate medications differently, therefore some require higher doses and some require less. I am currently at 1500 mgs of Neurontin a day and I am so glad I really gave it a fighting chance. I have seen huge improvement with my nerve pain levels.
My PM started me at a low dose taken in the evenings. This helped alot with the drowsiness. He was able to titrate me up, and incorporate some daytime dosing as well. I may have missed it, and if so, please forgive me, but I didn't see mention of how long you have been on the Neurontin. Has it been just a short time? If so, please do give it a good amount of time. I remember starting to see some improvement in about a couple of weeks, but again, my PM was titrating me up rather quickly. I'm also 5'2", and weigh 117 lbs, so my body definitely reacts fairly quickly to most medications.
I've not had any problems in taking the Norco along with the Neurontin, but I do stagger them, so I don't take them both at the same time. I allow at least a couple of hours between taking them. My doctor never told me I couldn't take them together, but once I found a schedule that helped and didn't make me overly drowsy, I just stuck with it. Some people notice results very quickly, and some people don't really show noticable results for a bit longer. Most of it depends on your body make-up, the actual dose of the medication and also how quickly your body is able to accept the titration schedule.
If the tylenol (APAP) in the hydro is too rough on your system, you might be able to speak with your doctor about a compounded hydro without the APAP in it. Some doctors are ok with doing this, and if you have a compounding pharmacy in your area, it might be worth a try. I have suffered with IBS since childhood and I understand exactly what you say about the tylenol messing with your stomach. There are many meds that really would help my pain levels, but because of the IBS they can't be used. Too much violent intestinal trauma.
I don't know that I've actually answered any of your questions, and if not, please forgive. Keep checking back though. There are so many people here who know so much more than I do. I just wanted you to know that your are not alone. Take care, and please keep us posted.