I'm not sure about the State that you live in, but when a doctor fills out a form stating "Unable to work until_____", that should serve as a legal document entitling you to take as much time off as he or she thinks is appropriate according to your injury. I'm pretty sure that you're going to have trouble with the Chiropractor not being able to see you during your absence, though.
I learned from experience (at least in my State, Pennsylvania) that I was entitled to seek medical attention from another doctor without having to wait on the Worker's Compensation Doctor's scheduled appointments. And don't quote me on it, but in a lot of cases, Worker's Compensation doesn't always view Chiropractors as credible sources when it comes to diagnosing a major back or spinal injury. My Father saw a Chiropractor for years until WC just decided that he wasn't qualified to prove that his back condition warranted SWIF benefits and they just stopped paying the guy. From the last I heard, he is still suing the company that my father used to work at for unpaid medical treatment.
I can relate with you on the issue of my former employer stating that I supposedly "Quit voluntarily due to illness." after my own SWIF benefits were stopped. If you really wanted to stick it to them, you could ask them to produce a letter of resignation or some other form of proof that you quit voluntarily, but it sounds like the only thing that you do have is that Doctor's note stating that you were unable to return until you were well enough to perform your job. As long as you have that note, you have proof that you could not return to work under Doctor's orders. I would definitely seek an attorney's advice on this matter.