LexisNexis couldn't find me at first, but the proper channels worked easily
This is kind of a "duh" post, with a lot of obvious details. I'm doing this for those of you who are neurotic like me and want to be TOTALLY SURE of how every step will go (at least based on my experience). Ideally, I would have liked to know that THERE IS HOPE even after mailing copies of my social security card and driver's license along with a request form to LexisNexis and receiving a disappointing "we don't believe you are you" letter from LexisNexis. Okay.
In this reddit post I mentioned how LexisNexis was continually unable to give me my consumer disclosure, due to failure to authenticate. I just wanted to let people know that the obvious solution (call them and do what they say) worked. I received my disclosure link in the mail within the specified timeframe! I will describe what I did.
Almost certainly: I will say "almost certainly worked" because I have not received my disclosure yet. Today, a customer service person (and I have found LexisNexis reps to be knowledgeable) told me that I would soon receive a link in the mail, which I could use to obtain my consumer disclosure. At the end of the call, I asked whether there was a chance that, instead of receiving a link, I would instead receive a letter requesting additional proof of identity. The representative said definitely not (although I might get some like that first, that were automatically generated by my earlier attempts to authenticate). If it really works, I will come back here and update.
What I did: I called the number on this page ending in "1", I got a human easily, and I explained to them that I had tried to get my consumer disclosure a few different ways (see my last post) but kept getting letters saying that my identity could not be authenticated. They tried to authenticate me again over the phone but that also failed. Then they gave me a case number, and told me to go here and send them a message with that case number, attach a photo of my social security card to that message, and then call them back and reference that case number. I sent them that message (I attached front and back of social security card, I don't know whether that matters), and I got a follow-up email (it went to my spam). That email contained a second case number. I called that same number ending in "1," got another human, gave them the first case number, told them I wanted my consumer disclosure and explained my authentication problems. They asked me for the second case number, then they asked me for some other basic information about me, including driver's license number. After that, I was successfully authenticated and told that I would receive a letter with a link in 7-10 business days. That link should get me to my consumer disclosure.
I've heard that there is something called a "full disclosure" which has a bunch of supporting detail (people have described getting 100s of pages). I asked about that, and the customer service rep told me that that was the same thing as my consumer disclosure. Take that for what it's worth, I don't know much about this.
Some people have speculated that the most likely reason for an authentication failure is that you don't actually have a file with them. I have definitely seen cases where someone failed to authenticate after providing correct basic information, but then later authenticated and had a non-empty disclosure. I'm not sure yet whether I'm one of those cases, but now we definitely know that my lack of a file was not the reason for my failure to authenticate. So there's one data point.