As St. Thomas, the greatest of all the theologians was wrong about the Immaculate Conception, the same is to be said about all the others who taught salvation through faith alone, which is a BOD - we know they were wrong because of the teaching of Trent.
Points to consider.......
1) It is with certainty of faith that we know that you, me, and all those who have ever been and ever will be baptized, are baptized via the Divine Providence. Almighty God *always* provides us with the time to do it, and the water for doing it, and the minister for doing it - always.
2) As such, you must believe that if God can arrange for you and everyone else to be baptized, that it is by that very same Providence that He can and will arrange for anyone else who desires or is willing to receive it and enter the Church.
3) When God made the sacrament a requirement for heaven, God bound Himself to provide the sacrament to all who desire it - even if that means a miracle - remember: what is a miracle to God? Nothing, nothing at all.
4) The only way a BOD works, is when God purposely withdraws His providence from the event. this means that with the divine providence, a BOD fails, without it, it works.
5) The condemned doctrine says that the recipient of a BOD saves themself, this idea is known as salvation through faith alone, which again, the Church condemns.
6) There is no getting around any of this if a BOD is to actually be salvific. You have got to take God *completely* out of the formula, which is what the doctrine of a BOD does.
You seem to hold a false dichotomy about Divine Providence. As if everyone He wills to be Baptized will be provided with all the ceremonies, in the cathedral on the next Sunday. Those who are baptized on Tuesday, or on their deathbed, on on the battlefield, or by a non-Catholic baptizer, or in any worse circuмstances are clearly being disfavored by God.
If all BOD and BOB are real, then it would make sense that God's Providence would allow precisely such circuмstances in order to demonstrate to all non-Catholics that they need not fear any circuмstance that could prevent them from receiving salvation when in any dire need.
We see this exact kind of Providence in the case of the Scapular. The Scapular says, "Whoever dies wearing this Scapular will not suffer eternal fire".
It does not say, "Whoever dies wearing this Scapular will certainly get his sacraments first".
If God's Providence works this way for a sacramental, why would He be more demanding for a sacrament for those in danger?
What happens if a non-Catholic puts on a scapular to save his soul, lest he should die without finding someone to baptize him, and then so dies?