Insurance lied to me about my coverage!

Okay so basically what happened is: I wanted to go to a different lab to get my blood work done because I had bad experiences with my old one. I called my insurance company (BCBS) to ask if a particular lab was covered under my insurance. They told me that yes, it was covered, so I went there a couple of times. Shortly after the second time, I finally got the bill for the first visit, approximately $1000. For blood work. Obviously I immediately call my insurance to ask what happened and why it wasn’t covered like I was told over the phone. The representative told me that they haven’t covered this lab that I went to since 2007. I was completely shocked because I was told that it was. They said they might have a recording of the phone conversation I had with the first representative (the one that horribly misinformed me) but didn’t hear much else about it. I sent in an appeal (even dated the time I originally called about coverage) but all I got back was “well, the claim was filed correctly”. Which is great, because obviously it was and that’s not the problem. The problem is I was lied to about my coverage and now owe ~$2000 for blood work. I called the lab I got it done as to see if I could get self-pay prices but they told me it was already processed through insurance so I’m out of luck I guess? That doesn’t really make sense to me. I’m working on writing a second appeal now but I just feel completely screwed over and BCBS doesn’t seem to care. Sorry this ended up being longer than I meant it to be, I just need some advice. Is there anything I can do in this situation other than just sending another appeal? Or anything I can add into my appeal to make them listen to me? Or even just a way to make this cost less in any way. Thanks for reading.

TLDR: Insurance company told me I was covered when I wasn’t and now I’m out ~$2000 over their mistake. What do I do??