Ahh the joy of split groups. The bane of any target shooter. My usual culprit is inconsistent trigger control. With springers shoulder pressure or padding. I got split groups when my sweat shirt would occasionally double over under the the butt pad. Doesn't take much with a springer, but it's usually something the shooter is doing. You'll figure it out.
I don't shoot at half breath. I usually get on target and shoot holding a full regular breath. Sometimes I switch it to shooting just after a complete exhale. My POI will be different between the two. The problem with shooting on a half breath is determining the halfway point. What exactly is half a breath? I like shooting with a full breath because I stay oxygenated while trying to steady on a target.
I agree on the trigger. Hard pulling takes away on siting concentration . Some times my thought goes to come on, come on, is this thing going to fire any time soon , surprise , fans it. or if hard I get a tad off to the right.