I have used the SAC die on GT and 223 for thousands of cases.
The top of the sizing portion of the mandrel has to be low enough so the brass isn't binding inside the bushing, but high enough that the mandrel engages the ID before the OD of the neck exits the bushing. Contrary to what others have said, this is intentional and should be set up that way to reduce runout in theory.
Possible options from most likely to least likely in my opinion:
1. The mandrel is set too high, binding the brass between the bushing and the carbide mandrel. If you can't go low enough, you may have the wrong length mandrel.
2. You're not getting as much lube on the ID as you think
3. The mandrel and/or bushing is the wrong size. Check mandrel size with a caliper and check brass thickness to determine bushing size
4. The ID of the die body isn't smooth
As for inconsistent headspace, this can come from inconsistent lube (probably not the case in your situation) or the die not having enough preload. They should be screwed in enough to where the die maintains contact with the shell plate through sizing.