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The problem with not believing in BOD and BOB and invincible ignorance is that it necessitates double predestination.

Invincible Ignorance isn't an article of faith and just because a pope mentioned its possibility (as a philosophical theory), doesn't mean it actually exists in reality.  In fact, Scripture condemns the idea in John1, where St John tells us that Christ "enlightens every man who comes into the world".  Since we know that every person is born with the knowledge of the natural law, and of God, then this means that God does not create anyone invincibly ignorant.  As St Paul tells us, God wills that all men are saved "and come to the knowledge of the Truth".  
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Since it is infallible that God wills all men to be saved, and it's infallible that Christ enlightens every person who is born, then it's infallible that there is no such thing as invincible ignorance.  Everyone has at least the natural knowledge of sin and of God.  This is sufficient, as grace builds on nature.  If one is of good will, and follows his God-given conscience, God will lead him to Truth and Catholicism.  
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The barbaric African or the Japanese or the American Indians were all damned for hundreds of years for lack of missionaries. That is double predestination, no doubt.

You correctly use the term "barbaric" because these peoples were savage, war-loving, evil tribes whose cultures revolved around killing, power, and paganism.  They did not follow the natural law, they worshipped satan (in his many forms) and most had some form of human/child sacrifice as part of their "religion".  
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The lack of missionaries weren't the problem; the lack of good will was.  As an example, even the most anti-catholic historians agree that the vast majority of US indians rejected catholicism because they were not a peaceful people and only wanted to fight their neighboring tribes over the best hunting ground.  

Without getting bogged down in the intricate theology of grace, it should be obvious to every Catholic that God is Infinite Love, and that it was His love that moved him to create man to share in His happiness, and that He loves every soul that He has created with an infinite love and desires its happiness infinitely more than we desire it ourselves.

God created no one to damn them. Every soul that is damned, is damned through its own free choice. "Before man is good and evil, that which he chooses shall be given him". How many saints and spiritual writers tell us that it is precisely this that constitutes one of the principal torments of the damned, seeing how easily they might have saved their soul if only, if only, if only they had responded to God's graces, which they failed to do through their own fault.

It is equally obvious that many souls created by God have lived and died with no knowledge of or contact with His one true Church, with absolutely no possibility of being baptized and belonging to that Church. These souls, too, were created to share in the life of God and to be eternally happy with Him in Heaven. These souls too, will be saved or damned by the choice they freely make.

The conclusion is obvious: The Omnipotent, infinitely merciful and infinitely loving God, is not constrained by the ordinary means that He has established to save souls, namely by being made members of His Church through Baptism, worshipping Him in the Holy Sacrifice of the Mass, frequenting the Sacraments... They will surely be judged on how they have lived according to the natural law and how they have corresponded to the graces God has given them. Who knows if God will not give one or another their own particular revelation with the opportunity to choose for or against Him.

Surely, it is this common sense Catholicism that Fr Cekada was alluding to.

Yes, Plenus Venter. I agree with you. God's Universal Salvific Will, revealed in Sacred Scripture in many places, is dogmatically certain: "Is it my will that a sinner should die, saith the Lord God, and not that he should be converted from his ways, and live?" (Ez 18:23)" "Even so it is not the will of your Father, who is in heaven, that one of these little ones should perish."(Mat 18:14). "The Lord delayeth not his promise, as some imagine, but dealeth patiently for your sake, not willing that any should perish, but that all should return to penance." (2 Pet 3:9), "Who will have all men to be saved, and to come to the knowledge of the truth." (1 Tim 2:4),

Calvinism/Jansenism are heretical because they deny this. St. Augustine and St. Thomas, as St. Alphonsus shows, and unanimously all the Fathers and Doctors, teach the doctrine of God's Universal Salvific Will, which also follows from the dogma that Jesus Christ Our Lord and Savior died for all. It cannot be reconciled with Calvinist heretical doctrines like limited atonement and double predestination. The Truth is that God loves us all and wants us to be converted to Him and be saved. This offends some who would like others to be lost. Hatred of neighbor and desire for others to be lost is a grave sin and never comes from true love of God or zeal for sous. 

The below site contains numerous references to Baptism of Desire. I cite only the holy Doctors St. Alphonsus and St. Robert here.
http://baptismofdesire.com/

·     St. Alphonsus Liguori, Doctor of the Church (18^th century): Moral Theology, Book 6, Section II (About Baptism and Confirmation), Chapter 1 (On Baptism), page 310, no. 96: "Baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment. It is called "of wind" ["flaminis"] because it takes place by the impulse of the Holy Ghost who is called a wind ["flamen"]. Now it is "de fide" that men are also saved by Baptism of desire, by virtue of the Canon Apostolicam, "de presbytero non baptizato" and of the Council of Trent, session 6, Chapter 4 where it is said that no one can be saved 'without the laver of regeneration or the desire for it.'" (Note: Unbelievers can see the original book in Latin here. Turn to page 310 in the book (or page 157 of the PDF file).

Moral Theology, Bk. 6, nn. 95-97: "Baptism of blood is the shedding of one's blood, i.e. death, suffered for the faith or for some other Christian virtue. Now this Baptism is comparable to true baptism because, like true Baptism, it remits both guilt and punishment as it were ex opere operato… Hence martyrdom avails also for infants seeing that the Church venerates the Holy Innocents as true martyrs. That is why Suarez rightly teaches that the opposing view is at least temerarious."

On the Council of Trent, 1846, Pg. 128-129 (Duffy): "Who can deny that the act of perfect love of God, which is sufficient for justification, includes an implicit desire of Baptism, of Penance, and of the Eucharist. He who wishes the whole wishes the every part of that whole and all the means necessary for its attainment. In order to be justified without baptism, an infidel must love God above all things, and must have an universal will to observe all the divine precepts, among which the first is to receive baptism: and therefore in order to be justified it is necessary for him to have at least an implicit desire of that sacrament."

·     St. Robert Bellarmine, Doctor of the Church (16^th century): De Sacramento Baptismi, cap. 6: “...among the ancients this proposition was not so certain at first as later on: that perfect conversion and repentance is rightly called the Baptism of Desire and supplies for Baptism of water, at least in case of necessity”....."it is certainly to be believed that true conversion supplies for Baptism of water when it is not from contempt but through necessity that persons die without Baptism of water.”

De Controversiis, “De Baptismo,” Lib. I, Cap. VI: “But without doubt it must be believed that true conversion supplies for Baptism of water when one dies without Baptism of water not out of contempt but out of necessity... For it is expressly said in Ezechiel: If the wicked shall do penance from his sins, I will no more remember his iniquities...Thus also the Council of Trent, Session 6, Chapter 4, says that Baptism is necessary in fact or in desire (in re vel in voto)”.