Rick has been right on target. I'd just like to add that from what I understand you have a LTD policy already in place. Being diagnosed already I don't think that you will be able to get, let alone afford a LTC plan.
Are your doctors supportive of your condition. If so is there any way that you can get STD either if it is your earned leave or otherwise until the LTD kicks in. The objective is to leave now under your terms, not theirs. PD will only progress, albeit however slow but stress from trying to keep a job only worsens this. Apply asap with a good paper trail of medical history, doctors, etc. It may take a while but it will be much faster if you have a good paper trail of records, then there is no denying your qualifying. I know that they can be idiots but PD is clearly outlined on the listing of impairments-

11.06 Parkinsonian syndrome with the following signs: Significant rigidity, bradykinesia, or tremor in two extremities, which, singly or in combination, result in sustained disturbance of gross and dexterous movements, or gait and station.

Last of all it never hurts to throw a few senators, etc into the fray- they're always looking for an ax to grind. I just wrote a letter to mine regarding mortgage modification. The bank flat out told me that they were not obligated and as such were not going to offer me a modification. Well, I was told my letter went to the comptroller of the housing issue at the federal level at the time. The next thing I know I'm talking to the executive secretary to the CEO of Bank of America!!! How's that ??!!