So I fought the final boss today and haven't been able to beat him yet.  My party is Lighting/Fang/Hope.  The first couple of tries, I wiped maybe a third of the way into the fight.  The third time I fought him, I managed to whittle him down until he summoned a Doom counter on Lightning.  Great.  Time to panic and die as I flail about trying to make that asshole stagger.
 
This is not a short fight, and since I turned the game off, I'll need to fight through the boss before him again just to get to him.  Does anyone have some useful tips for how to take him down?

 maybe I was lucky but I only died once though out the whole 3 part fight.  Damn that instant kill on the 2nd part.
I use your exact party setup as well, expect with Fang being Leader. (Commando seem more suitable as leader, plus she can Tank to avoid some big hit)
 
The best way to build up the stagger meter with this setup is   Saboteur /  Ravager / Ravager.  Just make sure everyone get Haste 1st and the fight should be extremely easy.
 Saboteur  slow down the meter just like commando and build it up as fast as Ravager.

Not to sound like a dick Hal <3 but his fight is fairly short. I beat him in either 3 or 4 staggers, never got the doom counter and none of my characters were maxed on any crystarium, I'm sure you can do the same. 
 
You probably can't have a strategy near mine unless you grinded some but here is what I did anyway: 

• Lightning/Snow/Hope
• My primary means of healing on this fight and what I switched too after every Merciless Judgement attack was Med/Sen/Med
• Started fight as Sab/Sen/Syn, buff up and get debuffs on him, specifically you want deprotect on him (though not yet).
• Be absolutely positive you get Veil on the entire party, do not make Hope a different class until you get this buff up
• Switched to Rav/Rav/Rav and built the chain up to near full (in roughly 1.5 rounds of attacks) then switched back to my setup class to apply deprotect, this is safer than applying it at the start because he has a long stagger meter and chances are it will drop otherwise.
• Finish off the stagger, depending on what attacks he was currently doing determined what I did from here. If he was still spamming the black laser beams I used Com/Sen/Rav, if the damage income was not that high I went with Com/Com/Rav. Going with Com/Com/Rav was excellent since with deprotect I could drain about 30% of his HP away each stagger, there was also the chance I would get 2 smite/scourges (someday I will remember which is which) and do 99,999 3 or 4 times before he was unstaggered.
• I then repeated this 2 or 3 more times (honestly can't remember anymore, but it wasn't long)  until he was dead. Remember you can use your summon as an Oh shit button if things go south, I had to near the end when buffs were starting to drop and I was debuffed to the extreme.

1) Start it by having a Syn cast haste (Com/Syn/Sen) or (Med/Syn/Sen)
2) Then change to Mystic tower (Sen/Rav/Rav) or Tri Disaster (Rav/Rav/Rav) or  (Com/Rav/Rav)
3) If you have to heal switch to Med/Com/Rav or if you're in real trouble Combat Clinic (Sen/Med/Med)
4) After staggering switch to  Com/Rav/Com and you should be fine. If you need to heal switch to 3)
 
I beat him on my first try. The 2 previous fights were harder. Good Luck!

I understand where you're coming from with this fight. Other people told me that they thought it was pretty easy but I couldn't for the life of me kill the second boss. I had to resort to somewhat cheap tactics, a party of Vanille/Light/Hope and set only a few paradigms based around Sab, Med and sometimes Sen. I just got Vanille to poison it and it was dead after 4-5 poisons.

My setup: Light/Vanille/Sahz

Strategy:

Start with a paradigm with SYN for Haste (Hope should be able to learn it),  a SAB (in your case Fang), and Lightning as either a COM or if you've put points in either SAB or SYN. Once Haste (at minimum) is up on everyone, begin the offensive. In terms of paradigms, a MED/MED/SEN paradigm (which you can do with L/F/H) will help for quick healing and damage reduction is helpful, as well as either a RAV/COM/RAV or RAV x3 (depends on if Fang can be a RAV yet) for stagger building, and a COM/COM/RAV for damage dealing once the stagger % is near 999. Also helpful paradigms are RAV/COM/MED for a mix of offense and healing, and RAV/COM/SYN for buffing while remaining offensive. 

5 stars with only main 3 roles on each character maxed but no upgrading done whatsoever.

From my experience, I noticed that the more commandos I had attacking Orphan when he wasn't staggered, the more times he used that damned ability that reset his stagger bar.  I think it was Temporal Hollow or something.  Anyways, once I started using tri-disaster the battle went a lot better for me

Sentinel is useless for the last couple fights because everything is aoe damage or negligible. I was shocked at how easy the last fight was and 5 starred it easily my first attempt. I use Light/Fang/Hope with Light as a Ravager with a second tier axis blade. I started the fight Rav/Sab/Syn and just kept spamming Army of One until she was staggered then switched to Rav/Com/Med to heal up before switching to Rav/Com/Rav to finish her off. I think my final time was 1:30 but it could be done much faster I think if you were paying attention to when you should switch.

" Sentinel is useless for the last couple fights because everything is aoe damage or negligible."

I had trouble too and I found it was because I was not doing enough damage and I didn't have enough health to outlast the DPS. I recommend grinding out some experience for a couple of hours and it'll be cake.

" I understand where you're coming from with this fight. Other people told me that they thought it was pretty easy but I couldn't for the life of me kill the second boss. I had to resort to somewhat cheap tactics, a party of Vanille/Light/Hope and set only a few paradigms based around Sab, Med and sometimes Sen. I just got Vanille to poison it and it was dead after 4-5 poisons. "

" and it's good to see that it didn't boil down to the same thing for everyone. "