As an anxious parent and an academic scientist, I did a deep dive into the peer reviewed literature on causes of SIDS when I first became a parent, which admittedly was a few years back.
I came across what is called the "Toxic Gas" theory of SIDS, which is admittedly not part of the major recommendations for avoiding SIDS in the USA- but I read all of the literature on it, and I found the evidence quite convincing, and the dismissals to be lacking. There were however dismissals in many popular review articles and mainstream recommendations, but they never presented an articulate rebuttal of what seemed like a reasonable concept, and convincing evidence.
The idea is that fungi in an older dirty mattress metabolize flame retardant compounds and produce toxic gases, which were measured in high concentrations with a mass spec on the surfaces of mattresses where infants had actually died from SIDS[1].
Other studies found correlations with mattress age after controlling for other variables, and decreases in SIDS rates with interventions based on non-permeable mattress wraps [2, 3].
Thinking about it fits neatly with some of the other risk factors you mentioned, as they reduce airflow, or put the infants face closer to the mattress surface.
I think it needs a lot more systematic studying, but it seemed convincing enough for me to buy a new mattress without phosphorus, arsenic or antimony containing flame retardants.
I'm not 100% sure about this theory, but I would not let any infant in my care sleep on an old mattress, or a mattress with potentially toxic flame retardants.
Surely there isn't one single "cause of SIDS" as it is just death, and any person can suddenly die at any age for any number of different reasons.
[1] Sudden Infant Death Syndrome: a possible primary cause
https://www.sciencedirect.com/science/article/pii/S001573689...
[2] Used infant mattresses and sudden infant death syndrome in Scotland: case-control study
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC131017/
[3] Cot Death—Cause and PreventionExperiences in New Zealand 1995–2004
https://www.tandfonline.com/doi/abs/10.1080/1359084040001683...