Long story short HireRight took so long with my dispute case that my job revoked their offer

Situation:

I still can't believe it has come to this point but this is a reality for me now. I got hired by a company that uses HireRight as their background check provider. After submitting info and documents it was about a week or two into the process that I noticed HireRight flagged me for having a Class 6 Felony. I do not have a felony so I immediately emailed them to correct this error and dispute it, only to be told I would have to wait until my background check fully completes. This was August 27th. They mentioned that the error would likely correct itself. Well, of course it did not and several days later the background check completed so I filed for the dispute. This was on Sept 4. I was supposed to start work on Sept 16th. It is now Oct 1st and I am still in the dispute process, so my work has delayed my start date each coming week as this process continues, which is currently tentatively looking to be Oct 7th.

I received a call from my company's HR department today asking me what was delaying the background check, which means HireRight has not been in communication with them like they have been telling me. Anyways, I filled them in and informed them of the situation. The HR lady was sympathetic with me as this is out of my control, but ultimately told me that they may move on if this process continues much longer as they need someone to fill the position for business needs.

From my understanding, HireRight legally has until Oct 4th to fix this error (resolve my dispute) due to FCRA regulations. I am hoping I receive some good news in the next coming days and I can finally begin work with this company, but in the event my offer is revoked, I am definitely going to pursue legal action against HireRight.

I moved to a new state and signed an 18 month lease after accepting this offer, so to be out of work for almost an entire month longer than anticipated and eventually getting let go without even beginning the damn job has been very difficult and stressful for me to say the least. I've had to work many odd jobs, pick up a part time job, and live on a very tight budget.

Question:

I don't know much about sueing or anything on legal side of things whatsoever, so I was wondering if anyone could help me here. I understand I should be looking for "background check lawyers" specifically, but is there a certain group or company anyone recommends? As mentioned I am low on funds at the moment so preferably I would need a practice that will not break the bank and is also good/can get me a good settlement.

Also, how much should I be looking to sue for? Is that a thing? I was thinking at least double my salary I was offered, moving expenses, living expenses during this month of hell, and then some for emotional damage and stress. I was thinking somewhere in the $200,000 range. Is that crazy?

Conclusion:

I have not consulted a law firm yet just because there is a chance all could work out and I begin work. In that case all is good, I won't sue. However, I just want to be prepared in case of the worst scenario that they go through with revoking their job offer I accepted.

Pray for me it works out as I was very excited for this job opportunity and honestly don't think I will get a better offer if I have to go back into the job market again.

Thanks in advance for any help/advice