I didn't have all that much when I applied really - I'd spent 2 years working Saturdays at a dairy farm, and ridden / worked at stables since I was 13, so that's nothing that you don't have by the sounds of it. Then I had done 1 week at a vet practice during school, and 2 more the summer before I applied. I had also organised a week at a zoo vets, but it hadn't actually happened by the time my application went in. I still got all 4 interviews though. There are people on my course (4 yr RVC) that have much less work experience than me, and they still got on.
Basically, it sounds like you're doing pretty well for husbandary experience already, though doing more can never hurt. Keep trying the practices as this seems to be where you need some more experience most - perhaps try ringing them? It's harder to turn you down on the phone, and shows commitment. And perhaps think about doing something more unusual - it's always good to have an interesting talking point for interviews.
If you want some sheep work, you can always come shearing in the Orkneys this summer - great fun and good experience too! (yup, can't oversell this enough - 2 of best weeks of my life were spent there last year!)