Hello and welcome. I'm sorry for all your troubles, continuing pain, and I imagine you'll remain conflicted for some time yet, while you're in this decision-making process. I'm not a lumbar patient, but it certainly does sound like your leg pain is some sort of sciatica irritation from your L5-S1 disc. However, have any of your doctors considered any of the non-discogenic causes of sciatica - see this link
www.sarapin.com. I think it would be worth while to read through the various syndromes mentioned in this article to see if any of them fit w/your symptoms. It's possible to have any one of these syndromes in addition to the L5-S1 problem.
I wouldn't give up completely on your neck. There are some people on this forum that have multi-level cervical DDD & have a combination of fusion with one or two ADR's. It can't hurt to get other opinions, but be sure you carefully research the proposed procedures/surgery, & be more than reasonably comfortable that it's the right plan for you.
I do think the neurologist suggestion to keep a journal is a good suggestion and a reasonable thing to do - at least while you're weighing all the options. Take care & good luck!
ML