I have 4 Proof carbon barrels, so I like them, but I think there is a difference between them and high quality steel barrels.
I have a 8 twist proof 7mm. It's 24" and sendero contour chambered in 7 SAUM. I'm shooting the 175 eldx and it does something similar to the original poster's. My cold bore is consistently .75-1.0 MOA high, then subsequent shots are around 0.4". Early on I thought "must be a scope issue" and have since replaced the scope. I have tested this enough times that the last test I ran I reproduced it at 1300 yds. My zero is for the 2-n shots, and I was able to get hits on steel at 1300 yds by using .75 moa less elevation on the first shot, and then moving it up .75 for subsequent shots and get 5 straight hits. I'm very convinced that I have a barrel problem on this one, but since it's repeatable I'm probably going to live with it. This rifle was built by LRI, so the craftsmanship is top notch and I've tried two scopes to rule scope issues out.
I have another proof on a 300 WSM that I'm having a weird issue with. On this one it shoots tight groups with my suppressor (0.2"-0.4"), but take the suppressor off and I get HUGE groups (like 2") and a huge POI shift (like not on the paper at 100 yds). I always test my unsuppressed shifts just in case I happen to need to take an unsupressed shot in a hunting situation, but on this rifle it's a disaster without the suppressor. I wouldn't even point it at an animal unsuppressed. This rifle was built by Crescent Customs, so also a top notch builder.
I own and shoot 7 different Thunderbeast suppressors and one thing I've noticed is that with a good steel barrel the POI shift is almost always nearly perfectly vertical, and quite predictable (like 2" high @ 100 yds unsuppressed), and often groups are still very good. With the proof barrels it seems like there's no telling what you'll get between suppressed and unsuppressed shooting. So it seems like the Proof carbon barrels have less predictable characteristics that good steel barrels. Another thing I noticed with Proof barrels is you have to run the exact same suppressor on them. When I shot only steel barrels I would switch between an Ultra 9 and Ultra 7 suppressor and not see any difference. I mean I literally would just grab whatever suppressor I saw first. With Proof barrels I get different POI's just switching from one ultra 7 to another identical ultra 7. So now all my suppressors are labeled to match the rifle they go on since I started shooting Proof Carbon barrels.
I still like the Proof barrels, but I'm fairly convinced they are a little more finicky than high end steel barrels if you put them up against target quality steel rifle barrels. It's just a more complicated thing to build than a steel barrel, so it makes sense that they aren't quite as predictable.