Testing gear:

Weapon: Diamond Musketoon (Savage Aim Materia VI x2)
Head: Diamond Helm of Aiming (Savage Aim Materia VI, Heavens' Eye Materia VI)
Body: Diamond Coat of Aiming (Heavens' Eye Materia VI x2)
Arms: Dai-ryumyaku Kote of Aiming (Heavens' Eye Materia VI x2)
Waist: Diamond Tassets of Aiming (Savage Aim Materia VI)
Legs: Dai-ryumyaku Jui of Aiming (Savage Aim Materia VI x2)
Feet: Diamond Boots of Aiming (Savage Aim Materia VI x2)
Ears: Genji Earrings of Aiming (Vitality Materia VI)
Neck: Carborundum Necklace of Aiming (Vitality Materia VI)
Wrists: Dai-ryumyaku Bracelet of Aiming (Vitality Materia VI)
Right Ring: Carborundum Ring of Aiming (Vitality Materia VI)
Left Ring: Dai-ryumyaku Ring of Aiming (Vitality Materia VI)

Total attributes were:

Critical Hit 1779
Determination 1270
Direct Hit 1766
Attack Power 2821
Skill Speed 814
Average item level 365

Testing procedure:

Auto-attack was used to activate turret attacks. I would then drop the target, although I would sometimes get another attack in by the time I had activated Hypercharge. Attacks without Hypercharge were roughly matched in hit count but not the main focus as normal turret damage was something I tested prior to this on a normal dummy (not SSS) and the damage spread was the similar. SSS was used to speed up gathering data points for Hypercharge values without waiting for the full cooldown. There was some extra variance in attacks because of 5% Vulnerability on the target and there was no attempt to normalize this because the magnitude of potency discrepancy was large enough to be easily observed (5% error vs 50% potency gain vs 100% expected potency gain).

Here's a video example of the procedure: https://youtu.be/6jAO0nHxbA4

If the sample size of normal turret attacks is a concern, here's a record of 330 hits in the same testing gear. Testing location was The Dravanian Forelands ( 32.8 , 24.7 ) Z: 1.0 Striking Dummy. Critical and direct hits were again excluded.

Hit count 330
Min 1480
Max 1634
Avg 1557

Multiplying the max hit 1634 with 5% Vulnerability modifier, we get 1715, which was the max hit from the SSS recordings. From this we can assume that the damage spread in both cases should be the same.