The item is completely gamebreaking and cannot have a value applied.
As you correctly identified, this item totally breaks the system mechanics. Artifact items are already beyond price, and this is stronger thanmaking it very easy for the wearer to achieve an artifactAC high enough to be nigh-untouchable. (There
There are a couple of artifacts that grant a flat +3 to armor, among other powers. +7 is off the charts and ridiculous.) Artifact items are already beyond price, and this is stronger than an artifact.
You can't calculate a gold value on an item like that.