That might just create a situation where the person goes through all this torture multiple times as they hold their breath and experience the pure agony until passing out only to wake up and have to go through it all again. It maybe seems better, but it's still basically the same torture.
Other than doing it TOTALLY unscheduled in the person's sleep, I cannot imagine a way you avoid the horror of this kind of execution method. And it's hard to even piece together a way you could practically implement unscheduled/in their sleep that wouldn't result in the person refusing to sleep, with sleep deprivation itself being a form of torture.