Nate:
I think there are two issues involved you might want to address. First, there is the bird in the hand issue. An admin fellowship is a prize and you won it by competing and being found a best available candidate. I am confident the learning has been valuable for the organization's objectives...make a promising administrator....and for you....discovering more about yourself. It probably comes as no surprise to you that fellowships are viewed as the best entree going for a career in hospital/health system management and being retained by a sponsor is quite affirming. Objectively, it seems you stand on the doorstep of something close to a "career sure thing" with, as has been stated by other correspondents, a road to higher rank and probably higher compensation than down the other route. Take the other path and maybe you are giving up something valuable. (I can imagine there are scores of early careerists who'd love to be standing in your shoes). We'll come back to maybe.
The other issue is who you are. Memphis looks like the biggest town you have spent time in based on your undergrad info and on your present place of employment. You need to know whether there is anything intrinsic in you to explain that trend, any pull toward smaller communities and smaller organizations? Did you like the optometry experience because it put you close to everyone...customers, other staff and let you make a difference hands on rather than through layers of other people? If so, maybe going into a practice admin position in the right community would be authentically (your generation might use "totally") fulfilling and so more rewarding than any other options your are considering.
Then there is maybe. Maybe there is a system that has an element that would let you be in the small organization/close to the pulse setting and still be part of a bigger whole. A role such as that might offer you later stage growth in status and income that looks attractive when you have a family and want to provide options for the generations before and after you. My implicit suggestion is that you should not necessarily accept the metaphor of a fork in the road. Road forks are usually envisioned as just two paths. Maybe you can blaze a new trail...albeit a private one that suits just you.
Here's an explicit suggestion. Think about taking the Career Anchors assessment we offer if you haven't done it already somewhere along the line. Some would say taking it now is premature, but you are in the place where validating what is authentically you may be well worth the effort. Here's the link: http://www.ache.org/CARSVCS/CarAnchor.cfm