I don't like flipping them over like that either. I think it's stressful and not a comfortable position for them. If you're not really careful, they can hurt themselves trying to get up off their backs. Rabbits have pretty delicate spines and if they twist the wrong way trying to get up they can actually break their backs.
To cut my rabbit's nails, I'll usually wait until they are calm and will give them something to eat or have my fiance pet them - just to distract them a bit. Then I'll gently hold each paw one at a time and as quickly as I can cut the nails. If you're having a really difficult time, you can make what's called a "bunny burrito" - basically you just wrap them up in a towel or a blanket so they can't scratch you or struggle. One at a time unwrap each paw out from the towel and cut the nails, then cover that foot again and move on to the next one.
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