I mentioned earlier that “Apostolic Digest” by Michael Malone was very helpful to me in resolving this situation in my mind. Fair warning, though - you might not like the answers it provides. My wife, for example, refuses to read this book, probably because she has Protestant family and doesn’t want to believe they are in any danger.
The modern Catholic Church is apostate and cannot give a straight answer on the matter (as evidenced by the many different opinions presented by Catholics on this blog). So the solution is to go back to what the Church used to believe before the days of modernism confused everything.
Apostolic Digest is about 160 pages of quotes (Scripture, Saints, Doctors, Popes, etc), and 40 pages of extensive references. (I believe every single quote is referenced.)
Here are some samples (in addition to the 3 ex Cathedra quotes mentioned by the OP):
But though we, or an angel from Heaven, preach a Gospel to you besides that which we have preached to you, let him be anathema! – Galatians 1:8
Work out your salvation with fear and trembling. – Philippians 2:12
All may be judged who have not believed the truth. – II Thes. 2:11
A man who is a heretic is subverted and sins, being condemned by his own judgment. – Titus 3:10-11.
Therefore, follow the bishops and priests. Apart from them, there is nothing that can be called a church. Anyone outside is impure; he is worse than an infidel. In other words, anyone who acts apart from the bishop and the priests and deacons does not have a clean conscience. For, all who belong to God and to Jesus Christ are with the bishop. Make no mistake about it: no one who follows another into schism inherits the kingdom of God. – St. Ignatius of Antioch - AD 107
Being placed outside the Church, and cut off from unity and charity, Heretics or schismatics could not be crowned in death, even though one should be slain for the name of Christ. Even if a man should deliver his body to be burned, he gains nothing. Baptism of blood cannot profit a heretic unto salvation, because there is no salvation outside the Church. – St. Cyprian - AD 258
Whoever is separated from this Catholic Church, no matter how much he believes he is living praiseworthily, will not have life, but the anger of God rests upon him. The reason is this offense alone: that he is sundered from the unity of Christ. – St. Augustine - 430.
If anyone holds to a single heresy, he is not a Catholic. – St. Augustine - 430.
This is the Holy Church, the One Church, the True Church, the Catholic Church, fighting against all heresies! He will not have God for his Father who refuses the Church for his Mother. No one can find salvation except in the Catholic Church. Outside the Church, you can find everything except salvation. You can have dignities, you can have Sacraments, you can sing “Alleluia,” answer “Amen,” have the Gospels, have faith and preach it, too. But never can you find salvation except in the Catholic Church. – St. Augustine - 430.
Some among the heretics flatter themselves with claims of martyrdom. But not all who submit their bodies to suffering, even to flames, are to be considered as having shed their blood for their sheep; rather, they may have shed it against the salvation of their sheep, for the Apostle says: “If I should deliver my body to be burned, and have not charity, it profits me nothing” (I Cor. 1:3). Indeed, as long as you remain outside the Church, and severed from the fabric of unity and bond of charity, you will be punished with everlasting chastisement, even if you were burned alive for the sake of Christ. – St Augustine - 430.
In the Catholic Church there are both good and bad, but those who are separated from the Church cannot be good. For their very separation from the Church makes them bad according to Our Savior: “He who is not with Me is against Me.” – St. Augustine - 430.
All the leaders of heretics have gone out of Christ’s Church to the synagogue of Satan, and they have passed over all together, disagreeing in their opposition to the faith, but agreeing in their leaving it. – St. Jerome.
To be subject to the Roman Pontiff is absolutely necessary for salvation. – St. Thomas Aquinas - 1274.
The unbelief of heretics, who confess their belief in the Gospel and resist that faith by corrupting it, is a more grievous sin than that of the heathens, because the heathen have not accepted the faith in any way at all. Hence, the unbelief of heretics is the worst sin. Speaking absolutely, the unbelief of heretics is worse than that of pagans or Jews. – St. Thomas Aquinas - 1274.
There is only one Catholic Church; this we firmly believe and profess without qualification. Outside this Church there is no salvation and no remission of sins. For at the time of the Deluge there existed only one Ark, the figure of the one Church. And all things outside this Ark perished. – Pope Boniface VIII - 1303
It is a sin to believe there is salvation outside the Catholic Church! – Ven. Pope Pius IX - 1792
Those who are obstinate toward the authority of the Roman Pontiff cannot obtain eternal salvation. – Ven. Pope Pius IX - 1792
People often say, “It is better to be a good Protestant than a bad Catholic.” That is not true! That would mean that one could be saved without the true faith. A bad Catholic remains a child of the family, although a prodigal; and however great a sinner he may be, he still has a right to mercy. Through his faith, a bad Catholic is nearer to God than a Protestant, for he is a member of the household, whereas the heretic is not. And how hard it is to make him become one! – St. Peter Julian Eymard - 1868
Many Protestants have almost the same practices as we, only they do not submit to the Holy Father and attach themselves to the true Ark of Salvation. They do not want to become Catholics and unite themselves under the banner of truth wherein alone there is true salvation. Of what avail is it, children, if Protestants lead naturally pure, honest lives, yet lack the Holy Ghost? They may well say: “We do no harm; we lead good lives”; but if they do not enter the true fold of Christ, all their protestations are in vain. – St. Frances Xavier Cabrini - 1917