Your Attorney is the best one to brief you on the situation. You DO have an Attorney as you prepare for Trial, right?
We offer general concepts, but you should give ALL your facts to a licensed Attorney in your state before you RELY upon any legal advice.
It sounds like there are issues that need to be decided by a judge, and it's likely that permanent disability is one of those issues. A rating is not the end all be all. There are legal issues such as apportionment and evidentiary issues that can reduce the amount of PD you're entitled to. Hopefully you have an attorney for trial to sort these issues out. Ask him/her.
So, there can be a number of reasons that the insurance company isn't paying you PD advances, despite there not being a dispute about the overall rating. If your employer took you back to work and you're making at least 85% of what you were at the time of the injury, changes in the law that took effect in January allow the insurance company to avoid having to start making payments until there is a settlement or award in your case. The same is true if you went back to work somewhere else and are making at least 100% of what you were when you got injured. It may also be the case that they feel that they have some sort of credit for an overpayment of something or for money you received from a civil lawsuit that they think they can use to reduce or eliminate what they owe you for your permanent disability. It may also be that they haven't accepted liability for your case, or that they are disputing the extent or existence of permanent disability on some other factual basis. It may also be that if they paid you money already, that they feel that they have paid as much as they need to given the value of the disability. (They are expected to hold out enough money to pay your attorney's fee, assuming that you are represented.) It may be that there are issues of causation or apportionment that they think will reduce or eliminate what you get for permanent disability.
I could go on and on making these guesses, but the best way to get an understanding of what is really going on is to ask your attorney. If you don't have an attorney, go talk to one right away. You can find experienced ones on this site or at CAAA.org, the organization for attorneys who represent injured workers in California.
a PD rating is one of many factors used / needed to achieve a resolution of your claim consult your attorney as what is the issue(s) in dispute.