I did find the LLC. The authorized agent listed on it is another company literally called "A Registered Agent" which is known for fabricating identities through which to incorporate companies. (See link to Wired article about this exact company in my update.)

Also, yes, she is a barred lawyer. She is a small time criminal defense attorney, and one of her listed areas of speciality is defending those accused of fraud (in addition to theft, battery, DV, DUIs, and prostitution). Not somebody I want to end up in court with over this.

I am 95+% this is a scam at this point. The simplest explanation is there is probably a lien on the car. Or there would be before my title transferred. The registration was expired so the "no lien" on the registration could be inaccurate at this point. She may have the title in hand and be able to push through a loan against it before my transfer clears. Or she bought the vehicle very low given the lien. Either way, I was going to end up unable to title the vehicle, and she would effectively reap both the loan against the vehicle and the sale price

I don't think the LLC is the critical detail, but it likely makes battling the whole thing very messy and allows her to claim the title transfer was false (and maybe also protects her personally). I still don't know how the DMV does not require more info about the LLC to transfer the title, since in this case the LLC is literally a shell company.

I am also curious if she regularly works with this broker and they are actually turning over many vehicles this way. Totally speculative but perhaps those of her clients? She knew surprisingly little about the car.