I like the 6.5 creedmoor, and think it works for what you want. Just a couple of thoughts based on the purpose of getting the new caliber. Ignore the rest of this if you don't want unsolicited advice on the topic of recoil shyness.
I am very sensitive to the sound and concussive blast. When it comes to reps with a lighter rifle, I've done that. I did it with a .223 bolt action so I could really separate the act of shooting from the flinch inducing noise and recoil. I am not sure if the 6.5 has enough reduced recoil to get you the benefit that you want. I was shooting my 7 magnum, my 6 XC/Creedmoor, and my bolt action .223. It was reps with the .223 and probably the thousands of rounds of .22 LR and dry fire that trained my body to follow the process of shooting instinctually so that it was automatic and not influenced by the flinch. The 6 cm is obviously less, but it wasn't as helpful as the .223 and .22 for me. It was during that time that I got a suppressor, so I don't know how much I can separate out its profound effect, but I know lots of dry fire and reps with .223 and .22 LR was extremely helpful to habituate my body mechanics and mind.
Have you considered spending the money on a suppressor instead of a new rifle?
It is easier for me to shoot a suppressed magnum than it is for me to shoot a braked 6mm. A large part of recoil shyness is physiological, and it is what the brain is doing without you knowing it. When there is a loud sound, sonic concussion, coupled with the physical recoil, it seems the obvious thing is to reduce the physical recoil, because it is what we are most conscious of. People have told me that they can handle the recoil, and that it doesn't affect them, but range time betrays them. I video tape their trigger break, I slip in empty brass, and they either admit/realize they aren't as manly as they think or they deny it. If they deny it, I casually just let them shoot and give them some pointers, but I don't even try to help them. Its only the ones who realize the truth that you can't train out reflexes, you can only adapt and minimize them.
You are admitting to the recoil shyness, so you have a huge benefit. the reason I say what I do, is that the brain reacts to the sound and concussive blast far more than the physical recoil. It is instinct and reflex deep in our lizard brains over which we cannot exert conscious control and we can't train out. I've found that most of us just aren't aware of it until we shoot with a suppressor. When we shoot with a suppressor and separate out the physical recoil from the loud sound and sonic concussion, it is much easier to shoot magnums and deal with the physical recoil. Ultimately, that is why people who shoot with suppressors don't go back to suffer through the sound and concussive wave, because that is the worst part of recoil. I can easily deal with physical recoil shooting a magnum with a suppressor until my arm is bruised and sore, and there is no flinch until I feel the pain. Once it becomes painful, the flinch comes. Consequently, I think that the sound and concussive blast is painful to the brain, though we don't register it like we do a bruised arm.