I’m new to the 6.5CM as well (T3x SL) and have chosen 129gr Hornady Interlock in a hand load as my chosen bullet for exactly the purpose you describe. Hornady sells this bullet in their Whitetail Classic ammo I believe - if you can find any.
I’d trust other opinions first but after my first 75 rounds downrange between 100 & 300 yards I’m shooting well under MOA with a super old school (but really great) bullet.
If its doing that well, I wouldn't change a thing. I have about 5 boxes of the 129gr Hornady BTSP interlock, but I mainly use them in my old military rifle (6.5 swede).