Don't be discouraged by the UC Davis rejection. For out of state, they mostly just look at GPA and their data suggests that they take only a few people below a 4.0.
Do you have something that you feel makes you stand out? A passion outside vet med, leadership positions, a well-rounded reason you haven't done research? It sounds like making a point to stand out have served people well in interviews.
My knowledge on this just comes from reading aaaallll the accepted students threaads. I'll be applying next cycle with similar stats to yours.
Congratulations on your great GPA and your many experiences. I'm wishing you luck!