I agree, I definitely tried not to double dip when filling out vet exp/animal exp/ etc.
I did list employment activities twice if they pertained to animals (ie, working as a vet tech and my research) - once under "Employment" and once under the other category to which it belongs (ie, "Research" for paid positions in labs). I thought about that a lot, but I decided it was important to show that it was both animal related AND that I was paid for it (which in my mind imparts a degree more weight to an experience, as you have certain expectations and responsibilities as an employee that you don't have as a volunteer). Totally personal preference, and it only came up for two entries, but that was the best way I could figure out to handle that.
Good luck!