I'm trying to picture this, you are running the GEC to XO in the transformer and then looping it to the ground lug, so your GEC is also your system bonding jumper?
Well inside your transformer your neutral must be grounded .
We have a 1/4" x 6 " x 24" inch copper grounding bar located in each remote electric room on the wall with insulators attached this is all connected to cold water ,building steel , and the ground rod system of the building which goes back to the main grounding electrode conductor at the main service with a full sized GEC.
I guess not thinking on most of our jobs we dont have just one transformer but multiple some rooms have two or three so we have to ground these when we hit the neutral with a bonding jumper in these transformers .
We bring the GEC connection from the copper grounding buss bar to the transformer also we use a buss bar crimp not a mechanical lug on buss bar
the size of this connection is the size of the ground needed on the secondary of that transformer not the full size GEC but the size for that secondary ground off that buss bar .
Now in the main electrical room our bonding jumper is inside the first disconnect or switchboard its a factory jumper a buss bar itself from neutral to grounding bar inside gear from there its grounding electrode conductor attached then it goes to the grounding buss bar on the wall of that room and then to each other electrical room .
But all transformers down stream are bonded with the same method .
We bring in the GEC to buss bar then to transformer go to the neutral first then loop it or bend it back down to the metal case of that transformer in one continuous un- cut conductor or wire from ground buss bar in room .