Yes, I have read those cautions about trancing a rabbit.
From all the years we've had rabbits, I never leave them on their back to watch their head fall away or tip backwards from their neck. An opposum might play dead for a sniffing mammal of a predatory species, but imo, rabbits aren't going to do so. To force a rabbit to be on his/her back for extended length of time is never - absolutely not - advised.
None of our rabbits were harmed by a burrito wrap for nail trims. Hope this helps.
98% of our crew is so acclimated to being held, and held in a snuggle towel, next to my chest. Hence, the slightly lowered angle of nail trim time doesn't upset them.
@Sweet Potato rabbit, similar to your technique, I continue talking and explaining what I am doing and reassure each bun.
There was a moment when one of our disabled girl's unexpectedly ******/retracted her foot away and her entire nail came out. Pressure applied, plus Kwik Stop, to stop the bleeding.