And at last we have the motive!

THIS^^^.  As the article that I cited explained thoroughly, this would be an example of contradictory intent, of intending to DO what the Church DOES, but intending (wishing, as you put it so well) for it not to have the Sacramental effect.

But I've not seen any theologians discuss the difference between intending the cause vs. intending the effect.  And my example of the gun clearly illustrates what you're articulating here as well.  I put the loaded gun up to a man's head and pull the trigger, while internally thinking that I do not wish for the man to be shot mortally in the head.  As you put it so well, that's just a wish or some kind of mental game.  As soon as I intend the cause, I am therefore also intending the effect.

I agree.  It's more than just presumed valid.  It IS valid.

See previous rebuttal.

I can perform an invalid baptism right now, simply by declaring outwardly “I have no intention to do what the Church does” then perform the form/matter.  I would simply intend to demonstrate how to perform an invalid sacrament, not to do what the Church does.

All the authorities are on my side against you.

There seem to be some here who cite obscure cases with no clear references, making sure to use untranslated Latin to make themselves seem clever, which essentially make the cult favouring claim that essentially reads the mind of bishops some trads don't like, and finds their intention wanting. It comes from the same stable as those who invented non una cuм, a horrifying error refuted by looking at an older missal where after the Pope and bishop, the monarch (who was often or always non Catholic, barring one or two deathbed conversions like Charles II). Obviously the ultimate point is that any one who goes to a chapel other than that of the cult leader or similar, goes to hell. The Plinioites who hate Archbishop Lefebvre do the same thing even though they usually go, at best, to diocesan TLM masses, like Attila Sinke Guimares who has such delusions that +Lefebvre had a personal masonic brass band, that +Lienart was obviously a freemason, and other delusions which suggest there is something in the water in Brazil. Who is +Lefebvre compared to holy Plinio de Correa?

By making that declaration, you're not doing what the Church does.  You're thereby taking it out of the context of an ecclesiastical act.  With +Lienart, we're talking about a situation where he showed up at a Catholic cathedral and conducted the ordination ceremony that by all appearances was an official function of the Church.  By declaring outwardly "I have no intention to baptize." you're actually adulterating the form of Baptism ex adjuintis.  You perform it in a CONTEXT which makes it quite clear that you don't intend to do it.  Just as if a couple people were goofing around pretending to be baptizing each other; the context there indicates that they are not intending to perform the rite but to merely simulate it.

If some diary entry of +Lienart came out tomorrow stating, "When ordaining Lefebvre, I deliberately withheld my intention." I would still not hesitate for one second to go receive the Sacraments from an SSPX priest that was ordained directly or indirectly by +Lefebvre.