Although the character's trying really hard, he still can't wield a too-big two-handed weapon in one hand
What stops the Medium titan mauler barbarian 3/titan fighter fighter 1 from wielding in one hand a Large two-handed weapon—despite his many special abilities allowing him to wield weapons of unusual sizes—is the restriction on the extraordinary ability jotungrip of the archetype titan mauler, which says
At 2nd level, a titan mauler may choose to wield a two-handed melee weapon in one hand with a –2 penalty on attack rolls while doing so. The weapon must be appropriately sized for her, and it is treated as one-handed when determining the effect of Power Attack, Strength bonus to damage, and the like.
Emphasis mine. The titan mauler archetype's extraordinary ability massive weapons allows the warrior to use 2-handed weapons that are inappropriately sized more easily, and so does the titan fighter archetype's extraordinary ability giant weapon wielder, but neither special ability changes how the special ability jotungrip functions, and that special ability functions only on appropriately sized weapons, and that's the one that would need to change for the character to use in one hand a two-handed too-big weapon.