A 1-level dip in Marshall would be worthwhile, assuming a decent charisma score. That would add Cha modifier rounds instead of just 5 from the Mighty Rage. Only worthwhile if the Cha score is 22 or higher. (note: build below doesn't care)
I forgot about Willing Deformity entirely.
So, 28 point buy Human: 18 Con, everything else is unimportant. Barbarian 11, Human Paragon 3, Stoneblessed 3, Dwarf Paragon 3
Feats: Endurance, Expert Swimmer, Willing Deformity (flaw), Deformity (Obese) (flaw), Reckless Rage, Extend Rage*5
Con at the end: 38 (18 base, +5 level, +5 inherent, +2 Silithar Bones, +2 Deformity (Obese), +2 Human Paragon, +2 Stoneblessed, +2 Dwarf Paragon). 46 (+6 Greater Rage +2 Reckless Rage) when raging.
Rage duration of 46 rounds (3 base +25 Extend Rage + 18 Con).
Remember, rage must begin at the very end of the duration of holding breath for maximum effect.
Rounds before any check is required: 139 (almost 14 minutes)
Modifier for Con checks made to hold breath: +26 (+18 Con, +4 Endurance, +4 Expert Swimmer)
22 rounds before the rage ends.
17 rounds of garunteed success for a garunteed time of 156 rounds (15 minutes, 36 seconds) 5 rounds to go before the failure chance suddenly jumps by 20% (total of 45% chance of failure when this happens).
Note: this build does not tap into Dragon material and only uses one "item" (the graft)