I put DS in his own room at 9 months and yes, he slept much better, but I wouldn't have done it before 6 months for that reason. My son was an awful sleeper, I probably got about 4 hours broken sleep every night and was exhausted but I didn't even consider putting him into his own room.
However, for 5 years prior to having him I had worked with a Health Visitibg Team and on a ward for babies aged 0-2 and had come across/cared for many babies who had died from SIDS and I was aware that the risk is very real.
Angelcare monitors will not prevent the baby from dying, they will just alert you once they've already stopped breathing.
Having "really good" baby monitors will have no bearing whatsoever on reducing the likelihood of SIDS - I'm not sure how those monitors are meant to reassure you that your baby won't stopped or hasn't stopped breathing just because there's a screen that you can look at and see your 'sleeping' baby....
I was once told that the science behind regulated breathing is that the levels of exhaled carbon dioxide by the parent in the air is what triggers the baby to breathe (though not sure if this is correct) and obviously if a baby is alone in its room then this stimulating factor to breathe isn't present.
We were fortunate though that we could fit the cot into our bedroom but if that wasn't an option I would have moved baby into the cot into its own room but slept in the baby's room myself too.
It's an individual choice and as has been said, just because x,y and z did it and their children were fine, that doesn't mean yours will be. It's just anecdote, that's all.
Its a decision for you to make as a parent as long as its an educated one.
My friend recently moved her newborn into his own room at 7 weeks and I found it hard to bite my tongue but I did because it was her choice to make.
And as has been said, children dying in car seats is from asphyxiation, not SIDS.