Just to interrupt, my son wears a helmet (although I prefer the term 'band' because helmet sounds horrible) as he has plagiocephaly.
This has been the biggest and hardest decision I have ever had to make, with lots of tears and fear, but one which was the right one, as our DS is now on the way to having a rounder head and we are nearing the end of this treatment. I have hated every minute of his head being in it, but know that it gives him a better future, without risk of bullying or ridicule or turning around to me one day saying 'why didn't you do anything?' No one wants their child to wear a helmet.
As for now, would I sleep any future children on their tummies having gone through helmet treatment? No I wouldn't. Flat head is treatable (although yes controversial, but everyone has to make up their own minds), I wouldn't risk SIDS.
What I would do is:
Sleep alternate nights, using a positioner pillow, so baby is on left, right and back. This will ensure each area is given equal degree of pressure
Use a pillow for nappy change, buggy etc
Use slings a lot more
Tummy time
Potentially buy a hammock for the early weeks, when they are most vulnerable.
Sorry for hijack, but I really cannot understand how anyone would risk SIDS unless their child totally preferred to sleep on their front/was the only way of them getting some sleep.
A bald patch will grow back. I don't think I've seen a baby without a bald patch.