Your rules are not taught by the Church and are much more stringent than St. Alphonsus'.
The only way a BOD works is when God's Providence is completely taken out of the formula, which is to say that with the divine providence, a BOD fails, without it, it works.
With the Divine Providence, God fulfills the desire by providing the sacrament, without God's providence, it is as St. Alphonsus says: the person's faith alone saves him - this idea is entirely protestant and condemned by the Church.
1)I am giving historical examples to illustrate my point, those examples are only one possibility. I don't mean that only people in the example I gave are subject to baptism of desire, but I am proving that baptism of desire must logically exist. I have purposefully used more stringent examples than the bare minimum in order to prove my point was solid.
2)I will quote Trent directly.
“If anyone says that the sinner is justified by faith alone,
meaning that nothing else is required to cooperate in order to obtain the grace of justification,
and that it is not in any way necessary that he be prepared and disposed by the action of his own will, let him be anathema.”
Someone with the Catholic faith but who refuses going to confession (despite being in a state of mortal sin) cannot go to heaven. Likewise, a Catechumen who does not desire baptism and who dies without being baptized would go to hell even though they have the faith.
The faith is necessary but it is not sufficient.