Sounds like you have sloppy chamber syndrome. Typical of Sako/Tikka.
Some have very good chambers and some have 'Friday" chambers.
I have two Tikka's and a couple of Sako's so know what I am talking about.
I have shot all the Berger 338 cal bullets and they all shoot well in my rifles except one Tikka which shoots just like your Sako but shoots Sierra's fine.
Just stick with what shoots in your rifle.
Do you reckon a good gun smith can recut the chamber as I am sitting on close to 500 bullets with no use at this point?