For the heart phase the ability breakdown appears to be the following, looking at the log:

14 Holy
15 Stone II
11 Ruin
28 Ruin II
8 Energy Drain
6 Aero
2 Aero II
2 Thunder
7 Bio
4 Bio II
1 Miasma II
8 Fast Blade
8 Savage Blade
6 Rage of Halone
23 auto-attacks by PLD

So judging by the 2.32 second auto-attack rate of Curtana +1, it took ~54 seconds to defeat Titan's heart.

Congrats to Snowy Wolf & Elrylith Marlithea for being the lucky healer pickups who got their SCH & WHM relics from our random spur of the moment FC Event. It was good fun. Just my luck that I blundered at 1% and was dead and that screenshot, but at least I was raised quickly and got one last Holy off to assist with the finishing blows.