I believe its the midwife that makes the difference.
I've had 4 births, no tearing or cutting. DS1 had a very big head, all of their head measurements were 75 centile I think. 3 were homebirths, and I agree that helped. MWs don't want to be stitching you up, its in their interests to get you through it intact.
Focus and listen to what the MW is telling you. It is crucial that you pant when she tells you as it controls the urge to push. Push before you are stretched and you will be more likely to tear.
Talk to your MW, tell her you want to avoid it, and really, really, really listen to her, although you will be thinking you are going to split in half and there is no way this is going to happen. When you are at that point, when all you want to do is scream and cry and refuse to do what she is saying, you have to. But, it is very nearly all over.
And you can massage your perinium with wheatgerm oil.