How do you refrain from letting the school admissions process stress you out?
If at all possible, identify a public school in your zone that you can absolutely send your child to if you want to. If you have a good back-up school you can rely on, you won’t be as stressed going through the admissions process for private school or gifted programs.
If you can’t find a good public school that you know you can send your child to, make sure you have a different back-up plan in case you can’t get your child into the school you want. Maybe it is moving to a better district or zone. Maybe it is moving to the suburbs or a different neighborhood. Maybe it is home-schooling your child. Maybe it is keeping him in pre-K one more year while you figure out a different solution. Nothing will make you more relaxed going through the admissions process as knowing that you have a good alternative in the event that things don’t work out as you want them to.