So the real problem is getting Medicare as a disabled person (less than 65)nwithout being on SSDI.
A person who has been certified as disabled by SS begins receiving SSDI then after 24 months on SSDI, they can get Medicare. Since you aren't getting SSDI, Medicare might have a problem getting you on Medicare earlier than 65 years old.
If you are vested in Social Security by the University job - seems you should be able to get SSDI but that might preclude your current disability plan - right?
Sounds like you may have to work this out mathematically for the best benefit to you all the way around - disability income and be best and most reasonable in cost health care coverage for yourself.
You may have to visit a local SS office to get the correct answer or at least talk to some sort of a supervision at the phone SS office - many of these folk just handle everyday type issues and yours is NOT an everyday issue.
In fact, add another call to your list - call the office of your Congressman and see if they can get you an answer after explaining all the details.
Good Luck -
It's Always Something . . . . Roseanna Roseannadanna