Arbitration generally is to cover property damages when the two companies have a dispute. As to your issues teh arbitration has no effect. You indeed should consult a personal injury attorney, though parking lot cases are tough.
Your question needs more facts to answer well, but a few comments, If you are exempt you do not have a right to overtime so the first thing that needs to be assessed is whether you are exempt. To be exempt more than half of your time must be spent on true managerial functions. For instance, if more than 50% of your time is spent on waiting on customers, ringing up sales, etc. then you are probably not exempt and your overtime is due.
Whether you are exempt or not is very fact specific and...
Your question is lacking in facts, but a few points. If you were doing work for which a contractor's license was required then the contractor might be your employer. You also might have the option to sue your employer civilly and also pursue benefits from the uninsured benefits fund.
If the letter bears on a disputed issue it is "information" and must be served on your lawyer 20 days before intended service upon the AME. The cases on this are numerous but for reasons I will never understand many practitioners miss the point. Trapero, Ferniza, Alvarez, Nedhar are but a few examples.
So the answer is no. I realize that in some areas each side sends their own letter, but that is not what the letter of the law requires as the cases on the issue point out.
The size of your employer is not relevant. They have no clout based on size and it is really the carrier on the hook anyway.
To me the biggest feature is avoiding a mill where your case will be processed by paralegals or other staff who are not lawyers. You have the right to expect your case will at all times be managed by a lawyer. The next feature is the ability to communicate with your lawyer rather than staff, which kind of dovetails with the first issue.