Yeah, honestly I think the problem is that PLD gets a zero cooldown stun.

The fight seems ripe for an interrupt rotation, i.e. WAR stuns first, DRG stuns second, MNK stuns third, etc. But PLD just blows that necessity out of the water with their global cooldown stun.

I feel your pain, it's really crappy to be on pure interrupt duty. Also if he's resisting on the 3rd stun it might be that your party members are using a skill that stuns them, as that will put it on DR more quickly.

IMO SE should fix this by fundamentally altering some skills.

Brutal Swing should have 20 sec CD baseline, and 3 second Stun baseline. Enhanced Brutal Swing should increase the duration to 4 seconds, and it should be cross-classable.

Shield Bash should be changed to a reactive skill (like Haymaker) that is available after you block and does say 140 potentcy attack with a high amount of threat for 40 TP.

What this would do:

It would make WAR more able to be on solo stun duty by reducing the CD, making it less likely to see it as "need at least 1 PAL for any fight with interrupts".
It would give DRG a niche by having 2 stuns off of the GCD in order to be on 100% solo stun duty, which should make slotting them in a raid a little more justifiable.
It would take pressure off of PLD to play a boring "stun duty" role with a stun that is on the GCD.
It would give PLD a much more active rotation and slightly more damage output.