Erin,
I completely agree with John about assessing the culture of your organization and with working with HR; and if needed work with upper management to demonstrate when and where remote work in similar positions has been successful. Two years ago I started the exact process and while it took time to work through, for the past year my team members and I have been able to work remotely one day a week. Sure, that's not the same as your situation, however we started with a nearly absolute no, so for us it's a significant step in the right direction. My point is, ask for what you want but be flexible.
Good luck!
p.s. I'm writing this while working remotely today!
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Michael Smith
University of North Georgia
michael.a.smith@ung.edu------------------------------