Hi Ocelot, welcome. I'm starting at Davis this fall, with a molecular & cell bio PhD. My situation was similar to yours - PhD from great university, great GPA (of course, because we've got a zillion research credits that are all A's - beware, adcoms know that grad GPAs are pretty worthless indicators of intelligence), high GRE score. I also had very minimal companion animal clinical experience (couple hundred hours in a shelter 8 years ago, 60-ish hours recent private practice shadowing).
BUT... There was a large clinical component to my research and the vet staff at our facility was very accommodating of my interest in vet med. So I had thousands of hours of research clinical experience, and a great letter from the head vet at our animal facility with whom I've worked very closely over the years. If your research involves animals (or even if it doesn't), get friendly with the head vet at your university's animal facility in the next year. Ask if you can watch or help out with cool stuff on other species in the facility, and get a letter from them.
I was strongly advised to get some private practice experience. I thought it was lame advice, but did it anyway. DO IT. Even the 60-odd shadowing hours I had were helpful. Every interview made it clear that they wanted to see I had some experience with companion animal private practice - I guess just because that's where so much of vet med is focused. Plus it let me say with even more confidence that that's not the direction I'm headed. 🙂
If your research involved animals and you did anything at all clinical - giving injections or collecting samples, doing surgery or dissection of any kind, or even just participating in their routine medical care - then aside from some token private practice experience you're probably fine. However, if your research was all petri-based and the entirety of your veterinary experience is volunteering at that one shelter, then... no, that's probably not enough. You're turning your back on a very expensive investment (expensive for the government agencies that paid your tuition and stipend, not for you personally), and the adcoms are going to want to know that you've got some really good reasons for wanting to move into vet med - and that you are actually going to stay there, rather than finishing vet school and then deciding to switch careers again. Not having much clinical experience of any kind isn't a good start to convincing them. Believe me, I understand your schedule constraints. 🙂 If getting more clinical experience means you've got to reduce your hours at the shelter, then you should consider that.
Good luck!