Neither FAQ directly addresses the question at hand. Those FAQs, as written, no more force you to choose between threatening with a spiked gauntlet and a two handed reach weapon than this FAQ says that you can't use armour spikes to make attacks on a turn in which you make attacks with a two handed weapon.
The first is explicitly about using that hand to perform a standard action that requires a free hand. There's nothing in RAW that says or implies that you need your hand free to make an attack with a spiked gauntlet--there are other "gauntlet" type weapons that explicitly forbid wielding weapons in that hand if it's not permitted, so the implication is actually that it's allowed with gauntlets, spiked and unspiked. And the same developer whose comment was turned into that official ruling has said that he would permit attacks with a gauntlet even if you're holding a weapon, albeit at a penalty. I linked to it already, but nobody addressed it. If you can attack into a square, you threaten it.
The second is about using the haft of your weapon as an improvised weapon, allowing you to ignore the "doughnut" with the same weapon. It only really applies if you insist that you need to adjust your grip to hit with the gauntlet.
If you want to read that interpretation into those FAQs for whatever reason, that's your prerogative and it's none of my business how you choose to play the game, but it's not a settled question and nobody must play the game that way in order to play by the rules. Repeating the same interpretation again and again doesn't make that interpretation any more definitive than the last--literal--hundred times it was repeated on the boards. I'm asking for you to give me a real ruling, since you're convinced that it works the way you say it does.
So, I ask again: show me where, please.