Every rifle is different, my S20 could love PH factory Ammo and yours could hate it…so I don’t know that anyone’s answer could be of much help. What any one guy suggests, may not work for that rifle. Best thing to do is to get as many different types of ammo as you can, and see which one your rifle likes the best. In the process of doing that, you may get a couple boxes deep anyway. They don’t require break in, according to Sako, but if you really wanted to “break in” your barrel correctly, make sure you clean it between every 3-5 shots, or in your case, between each different type of ammo. Probably wouldn’t be a bad idea to then shoot a fouling round, and then shoot your 3 shots for groups….clean, repeat.
Check your twist rate too, make sure it’s good to go with the bullet weight you’re using.
I’m no expert, but that’s what I’ve learned through experience. I’ve also got frustrated enough to sell that rifle and get another that shoots what I want how I want. To each their own. I actually just did exactly that with a weatherby vanguard, and acquired a Sako S20. Haven’t been able to shoot it yet though.
For what it’s worth, try to get your hands on some nosler partition, or accubonds. I’ve had good luck with those and the Hornady PH that you are having trouble with now. Play with your bullet weights too.