Double Weapons: A character can fight with both ends of a double weapon as if fighting with two weapons, but he incurs all the normal attack penalties associated with two-weapon combat, just as though the character were wielding a one-handed weapon and a light weapon. The character can also choose to use a double weapon two-handed, attacking with only one end of it. A creature wielding a double weapon in one hand can’t use it as a double weapon—only one end of the weapon can be used in any given round.
The combat two weapon fighting rules state
If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon.
The two weapon feats do not change this wording, simply that the attacks by your offhand are reduced. However as demonstrated by the double weapon, a single weapon can be used for both attacks.
There is an FAQ
What kind of action is it to remove your hand from a two-handed weapon or re-grab it with both hands?
And answers that both letting go and re-grabbing it are free actions.
So the question is, would you be able to adjust your grip and use two handed weapon with two weapon fighting? I except that the answer to this will also answer if a single one handed or light weapon can be used for TWF if you switch hands.