'Person who has planted the 'Seed'? Could this be me? I hope so. I'll answer the question anyway.
The gun balances where it balances until someone (with luck, a master such as yourself) adds, removes,or redistributes weight. The issue is reference point, not where it balances. You can reference to hinge pin, breech face, trigger guard, muzzle, butt, grip cap, stock oval and all points between. The reason for selecting (front) trigger as the reference point is to allow direct relevance to hand placement and to allow a consistant measurement among all types of guns. Pumps and autos don't have hinge pins, but they surely do have a balance point; could happen that a shooter would wish for commonality or comparison of balance between a pump and a break-open gun.
I would never tell someone the actual location of balance for his own guns. I will, however, tell him the best way to reference it. Your customer needs to work out with you what location of balance he really wants. I suggest that the two of you use distance in front of the (front) trigger. The average for 6 1/2# game guns is 4 1/2" from front trigger to tetter-totter balance point. That is near the hinge pin of many guns and not so close on others. I'd bet your customer has spent a fair sum of time and money on determining his desired stock dimensions. Have him spend a little time and, possibly, money on determining the handling characteristics he wants. For sure he should know desired weight and location of the balance point. If he wants to dig deeper, the he should learn desired swing efforts.
I hope it is clear that I do not recommend having the balance point at the trigger. I do recommend referencing balance point to the (front) trigger, just as LOP references the trigger. Everyone surely understands that the LOP reference from the trigger is not a recommendation that the butt be located at the trigger.
Please post back it there are remaining questions.
