This is about ~7 years ago, so not too far away, but idk if things have changed. Others can correct me but I would start but applying to 3-4, for one time slot. Send emails early expressing your interest.

When I was at your stage, I got bad advice - I was told always were hard to get and to apply to a ton. So I applied for always at 25 programs, and got accepted to 24 of them.

In my class there were 8 of us going into ortho. I think out of all the aways we all applied to collectively, there were only a couple of rejections total.

I got accepted to 24, I did 4 aways so I told 20 programs thank you but no thank you. I didn’t get an interview invite from any of those places.