Ellie is wiggly during exams too.
This is how I see it. Positive reinforcement is great. Proper restaint is not negative reinforcement though. I wouldn't say you need to force her on her side and hold all four paws right now. Start slow. Do one thing at a time. But in my opinion, getting a dog used to being restrained and even putting it in uncomfortable (by that I don't mean painful) positions is not a bad thing. If I just let Ellie decide to not be restrained at home, then I'm not quite sure how her teeth would get brushed. It isn't her favorite. And how would I give her SQ fluids if I let her walk around and do what she wants? Be safe about it, but don't let her do what she wants to either.
And treats are great. If you start small and are consistent, then positive reinforcement may work very well.