First, I second the experience that most production managers come from the tech side (SMs, TD's, design background). The people I know with degrees in Arts Admin are Managing Directors, GM's and Company Managers.
I love tuition remission - paid for my last year of undergrad. But what are the demands of the program vs the demands of your job. I had a great boss who didn't care WHEN I got my work done as long as it was done. I was also able to take a lighter load to balance my full-time employment.
Just some ?'s to throw out there:
Do you have to be enrolled in a degree program to be eligible for the tuition remission? If not, can you take a class in the arts admin field to see if it's really what you want/expect, before putting in all that time? Or do you know that you are interested in Arts Admin but having a hard time letting go of stage managing?
Just because there are more job prospects, doesn't make it right for you.
Finally, If it weren't free, which one, if either, would you be willing to pay for?