If that's the entire contract I don't see anything in there promising that you'd be successful at the job or that your duties would be one thing or another or that they wouldn't change for the better or for the worse.

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Given my diminished role as a result of all internal customer activities ceasing due to the merger and my department's noticeable lack of inclusion in the new org structure, how successful could I be in claiming involuntary resignation (this agreement only mentions voluntary resignation)?
Not successful at all. Any time you accept any job there is always the possibility that the job will change in ways that you don't like. That's how work works. I've had it happen to me lots of times. My recourse was (as is yours) to find another job elsewhere.

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Given that I have a disability (Type 1 diabetes) and my health has gotten significantly worse since joining this company and dealing with the relo and merger processes, as well as the indefinite period of uncertainty, what say you about claiming a disability to continue working under these conditions?
I don't think anybody will buy it since it's a pre-existing condition and everybody gets stress on the job.

But if you feel that the job stress exacerbated the diabetes you are welcome to consult a workers compensation attorney.

Bottom line, I think you are stuck with the one year requirement unless your employer fires you. And I suggest you be real careful about giving him a reason because he might just sue you for the relo anyway if he suspects that you just slacked off to get yourself fired.