No, at least you're not going to get that ability from Two Weapon Fighting, Improved Two Weapon Feint, or any of the other feats you've listed.
Improved Two Weapon Feint opens:
While using Two-Weapon Fighting to make melee attacks...
Emphasis mine, but it's clear that you must be using a melee weapon, and that you must be in range to make melee attacks with it. You might be able to cheese some range with a whip or some other reach weapon, but RAW does suggest that you're attacking with the melee weapons you're feinting with.
One of the answers on the thread you linked in your question list a couple feats that explicitly allow for feints at range, which again implies you can't do that with the normal feint ability.
could I swap my mainhand melee for a ranged weapon, and still get the benefit? Or do I need to *keep the melee weapon?
Unless you gain it through some other feat that explicitly allows it, you cannot exploit the bonus from a feint with a range weapon. Let's look back to the actual feint ability:
If successful, the next melee attack you make against the target does not allow him to use his Dexterity bonus to AC (if any).
Improved Feint lets you feint as a move action. Two Weapon Feint lets you replace your first attack with a feint "while using Two-Weapon Fighting to make melee attacks", that is the rest of the attacks you make that round must be melee attacks.