It sounds like you're researching this yourself alone and that is not wise. Before you convince yourself that you have no case because of your own research, consult with an experienced local personal injury attorney. You may (I stress "may") find the SOL begins to run from the date of discovery and not from the date of the injury.
This is not intended as legal advice but as educational information only. One should seek independent legal counsel.
You need to consult with a local medical malpractice attorney. The facts that you set forth are unclear. However, it would probably be very difficult to find that a statute of limitations is unconstitutional as it applies to a single case.
Perhaps, but the attorneys fees would be staggering and the courts are loathe to take rights away from doctors who have lobbies and money. And statute of limitation cases are constitutional or the whole system would break down.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none.