Turning them on their back is not trancing. They are not chicken, and even with chickens cou need to to some more than that.
I do it for sexing, and as a way to carry them when they are grumpy and would struggle, bite and fight in other positions. They are not tranced, they just can get no foothold and their body is well secured from struggling.
There is nothing that indicates to me that this position is more stressful than other ways, or having them struggling and biting, in the contrary, they know and accept that I have the upper hand now. It's the safest way for both of us. They are not less alert, or hypnotised, or whatever, they are just on their back and are being carried, it's rather rare that they are happy about that anyway.
All my about 100 kits nursed on their backs, none drowned. Some up to 16 weeks (hillarious sight), so also even almost adults can drink on their backs. And some rabbits do flop on their backs when relaxed. And rabbits are not stupid, they are not thinking you're a predator about to kill it, well, not if it's your rabbit and when it's used to be handled. But that's true for any way to pick up a rabbit.
But as it is, all rabbits are different, and some seem to have triggers that set of stress or even panic. Everyone knows his rabbits best. Also, they need to learn being handled that way, the first times many are surprised and struggle if you let them, but like with many new and somewhat unsettling things, start with short periods, low to the ground (in case it's better to let go) and a little treat afterward.
And it's more to it than just putting them on their back, think in advance where to put which hand, and maybe practice with a stuffed toy, the cat, or a mellow slob.
I carry them with my left, hand on their butt, with my other arm on their belly and hand on their breast, a finger toward each shoulder. Do not bend your face down, that hind legs of a 9lbs rabbit have quite some reach and incredible force.
All that said, I don't do it for fun, it's a last resort, none of my rabbits really like being picked up and handled much anyway. But rabbits are different, when one enjoys a noserub while on it's back, why not.