I recall a rather tragic case study published of a young lady, who in the grip of mental illness, committed suicide on a hospital ward by suffocation - she had stuffed reams of lavatory paper down her throat and completely obstructed her airway. The case study stated that this was not an uncommon occurrence among residents of the psychiatric ward, although all attempts had previously been thwarted by the body's instinctive reflexes (survival instinct) causing them to remove the obstruction.
This particular young lady, however, had been quite heavily sedated as a result of the high dose of anti-psychotics she was taking and it was observed that her consciousness was impaired, therefore her reflexes also, in a manner not dissimilar to that of a heavily intoxicated person. She was witnessed writhing in obvious physical distress for a period of time before she lost consciousness, soiled herself, and her movements became myoclonic. Staff were unable to revive her.
I've always felt it tragic to think of the pain and distress that young lady must have been in, I wonder whether she had the wherewithal to appreciate the seriousness of what she was doing and I think back to my own experiences of grave panic at the merciless hands of the hypercapnia alarm response during an attempted hanging and an accidental drowning, two of the most distressing and painful experiences of my life.
It's probably not the dumbest method one could imagine, especially if we're considering satirical answers, but to me, it is one of the most tragic I've encountered in the literature over the years.