Conjured item are still made of aura. "Solid" aura if you want, but is still aura. And it's not about "not seeing them" but not being able to feel as it's actually aura.
A silly example: Kurotopi probably has In on its conjured items. When Killua faced the building, He knew something was off, but He coudln't tell which one was the real one and which were the fakes. That's because "In" hide its true nature.
As for why is an application of Zetsu...I guess the "feeling" should be the same, as it's a way to contract aura.
If conjured items are solid aura as you say, then you can see them through with Gyou or even bare eyed provided you have Nen pores awakened. In Kortopi´s/Killua´s case had Killua used Gyou he would have seen the real hideout, which is bad in a hindsight, because Ryodan knew Killua and Gon knew Nen, so why would they use conjuration that would be seen through? Also if he had In on the conjured items, then the items would be invisible, since when Kurapika placed In on his chains then the chains themselves became invisible. This leads me to believe that Conjured items are not a solid aura. You change your aura into a material thing, albeit with special abilities.
I already addressed that Togashi´s functional leap of logic is too big for me. Zetsu doesn´t involve the manipulation of aura, you just close the nodes.
You and Ener9y are prying into this too hard, it's almost like you are out to prove togashi is a fool for In and are just not paying attention to reason. You say that Gyo "breaks" In but that's a poor choice of words. Remember in the Heavens arena when Zushi used gyo he could only see some of Hisoka's strands while Killua could see more, which proves that there are different intensities to both (which further supports the mental suppression theory).
In isn´t bad per se, but the origins and the execution of it are sorely lacking. If there are levels of Gyou (which, going by the example you use, there most definitely are), then how are they differentiated? By the amount of aura gathered in the eyes (imagine Meruem focusing all of his aura, probably in millions, into his eyes), or the quality of the aura (I think we had this kind of discussion before), then how do you determine the said quality of aura? Then this leads to a valid reasoning that there must be levels to "In", but then again why would Hisoka use an "In" that can be seen through by a Nen user with a minimal amount of skill/experience?
For some reason you seem to think that mental suppression is too hard to believe but it's really not. It probably involves making your aura neutral like Zeno in front of Meruem and dulling and suppressing your aura and the power/emotion/intensity it emits which is the same concept as Zetsu, which explains why its an advanced application of it.
Mental suppression is okay, but Zetsu is closing your nodes, how does that translate into changing the visibility of your aura? The Zeno example is bad, the hostility lowering is connected to the enmity, spiritual side of Nen not a technical one. Zetsu for the n-th time is not dulling your aura, it is closing off your nodes, which RESULTS in not leaking your aura outside, it does not change the property of your aura that is inside you.
As for why In works on conjured items you have to remember that conjured items are made from aura originally and still project a users aura after they are made (remember when gon and killua sensed the powerful aura of Kite's scythe). And if they can emit the users aura they can be suppressed the same way you suppress any other hatsu with In.
I think they sai they have a bad feeling about that scythe, which doesn´t necessarily pertain to Nen. If Conjured items project an aura of the user then when does that item run out of said aura? Remember the discussion Ryodan had about Chain user´s ability? The whole thing would be moot because with just one Gyou, or even without it since the nen users can naturally see aura with no In on it, the nature of the ability would be made apparent. Hell, if the aura projecting were true, then Machi would have seen the aura as Uvo was being kidnapped by Kurapika!
As for the numerical values for nen they don't take away anything from it. In fact they add to it by filling in some of the holes in nen, like how a specialist like pitou can be faster and stronger than an enhancer like Uvo. And togashi never forgot any of the other principals of nen they still fit in perfectly after he expanded nen with the whole numbers thing and it was really for the better.
Let me pose you a simple question; If Gon gathers 500 aura in his fist and Netero gathers 500 aura in his fist, provided that the force of the punching motions are the same, which attack would be stronger? About forgetting the principals of Nen, I was talking about you, you can´t simply disregard the inner working of Nen at your convenience - since you said that we should disregard them at unrelevant times.
In is only an advanced application of Zetsu because it uses the same principal (dull/suppress) but doesn't actually use Zetsu physically (the act of closing pores) which is why it must require mental control like Ten.
If the In doesn´t use Zetsu physically then why is it considered an application of Zetsu, since THE ONLY THING ZETSU DOES IS CLOSING YOUR NODES, the dulling part is just your delusion, the quality of the aura is unchanged when in Zetsu, it just doesn´t come out - this is still unanswered in 4 pages! Well all Nen is controlled mentally, there is a spiritual influence but not control.