We have an instance of BoD in the Eunuch of Candace (Acts 8).  He had "come to Jerusalem to adore."(27)  We know that this man at least knew of the religion of the Jєωs and sought to adore the God of the Old Testament.  We do not know his motives, but presume his sincerity, since God saw fit to send an angel to Philip, commanding him to go to "the desert," "the way that goeth from Jerusalem into Gaza."  The Holy Ghost had obviously stirred up the soul of the eunuch.  The Eunuch had been to Jerusalem, but had not heard about Christ there, and leaving the city he had a "desire" to follow the truth.  The Eunuch was reading the truth, but did not understand the truth, hence his admission, "how can I (understand the truth), unless some man show me?"(31)  And the Eunuch, after he had been preached to, admitted his belief in Christ, "I believe that Jesus Christ is the Son of God."(37)  Because the eunuch desired to know the truth, God confirmed the full truth (Baptism) in him.

Why on earth do BODers think Trent concludes the doctrine with John 3:5 "as it is written?"

You keep misusing the phrase, "as it is written".  This simply means that Trent is using 3:5 as proof for the prior statement.  It's important because John 3:5 disambiguates the "without A or B" expression, but it's not being used in the sense that you've been using it.

Of course the eunuch knew about baptism, it was he who asked for it ...

Of course the eunuch knew about baptism, it was he who asked for it, "the eunuch said: See, here is water: what doth it hinder me from being baptized?" (36)  And Philip the deacon, beginning with the Isaiah quote "preached unto him Jesus." (35)  I can only assume that Philip preached the Incarnation and the Trinity, what else would it mean to "preach Jesus"?  I argue that in the history of the Church there might not be a clearer example of a person who "desired" baptism more than this eunuch.  In the space of several hours he went from being a pagan to becoming a member of the Church, all because God fulfills his promise, "knock and it shall be opened."

The administration of the sacraments end when time ends.  Of course St. Thomas talks about the Eucharist continuing in heaven, etc.  I personally believe, and the Church has never defined, that on the Last Day, those who may have not been baptized with water (should they actually exist), will be baptized with water before entering heaven.  Provided there are human beings and water, baptism is possible.   

The Catechism of Trent provides the solution to your interpretive dilemma:

Regarding Infant Baptism

"Since infant children have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death."

Regarding Adult Baptism

"On adults, however, the Church has not been accustomed to confer the Sacrament of Baptism at once, but has ordained that it be deferred for a certain time. The delay is not attended with the same danger as in the case of infants, which we have already mentioned; should any unforeseen accident make it impossible for adults to be washed in the salutary waters, their intention and determination to receive Baptism and their repentance for past sins, will avail them to grace and righteousness."

The Church, in its gold standard Catechism, written by the same theologians who wrote the Council of Trent decrees, interpreted the phrase "aut ejus voto" as you say that the "BoDers" do, namely that "either one suffices" in the case of adults.

The Catechism of Trent provides the solution to your interpretive dilemma:

Regarding Infant Baptism

"Since infant children have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death."

Regarding Adult Baptism

"On adults, however, the Church has not been accustomed to confer the Sacrament of Baptism at once, but has ordained that it be deferred for a certain time. The delay is not attended with the same danger as in the case of infants, which we have already mentioned; should any unforeseen accident make it impossible for adults to be washed in the salutary waters, their intention and determination to receive Baptism and their repentance for past sins, will avail them to grace and righteousness."

The Church, in its gold standard Catechism, written by the same theologians who wrote the Council of Trent decrees, interpreted the phrase "aut ejus voto" as you say that the "BoDers" do, namely that "either one suffices" in the case of adults.

The Catechism of Trent provides the solution to your interpretive dilemma:

Regarding Infant Baptism

"Since infant children have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death."

Regarding Adult Baptism

"On adults, however, the Church has not been accustomed to confer the Sacrament of Baptism at once, but has ordained that it be deferred for a certain time. The delay is not attended with the same danger as in the case of infants, which we have already mentioned; should any unforeseen accident make it impossible for adults to be washed in the salutary waters, their intention and determination to receive Baptism and their repentance for past sins, will avail them to grace and righteousness."

The Church, in its gold standard Catechism, written by the same theologians who wrote the Council of Trent decrees, interpreted the phrase "aut ejus voto" as you say that the "BoDers" do, namely that "either one suffices" in the case of adults.

Nay, this delay seems to be attended with some advantages. And first, since the Church must take particular
care that none approach this Sacrament through hypocrisy and dissimulation, the intentions of such as seek Baptism, are better examined and ascertained. Hence it is that we read in the decrees of ancient Councils that Jєωιѕн converts to the Catholic faith, before admission to Baptism, should spend some months in the ranks of the catechumens.

Furthermore, the candidate for Baptism is thus better instructed in the doctrine of the faith which he is to
profess, and in the practices of the Christian life. Finally, when Baptism is administered to adults with solemn
ceremonies on the appointed days of Easter and Pentecost only greater religious reverence is shown to the
Sacrament.