All of this to say that the proposed syllogism collapses. The Bible may have a teaching on the relationship between God's desire for the salvation of all and predestination (I think it does, but it is radically different than the Reformed tradition has led us to believe, about which I hope to write more soon -- it has become a summer book project for me), but it is anything but "clear." The final premise neutralizes the first.
Is there no hope? Indeed, there is, but it requires a radically different approach to the Scriptures.
The author of the Scriptures is, at the ultimate level, the Holy Spirit. "Who spake by the prophets" as the Creed puts it. Or as St Peter describes, "For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit" (2 Pt. 1:21). Modern interpretive methods rely on the human element of the text: the historical context, the literary genre, the cultural background, etc. These are good things, but they partake in the fallenness of the world (an important point brought up by Pete Enns, although I think he goes too far). These methods are essentially apophatic: they tell us what the Scriptures cannot mean, but not what they do mean. It is only as the fallen creational condition of the Scriptures is purified by the Holy Spirit (only thinks here of the role of the Spirit in the conception of the human nature of Jesus) that progress to the meaning and application of the Scriptures can be made. There is no correct interpretation of the Bible apart from the Holy Spirit.
If we are to interpret the Scriptures aright, therefore, we need to acquire (or better, be acquired by) the Spirit of God and Christ. Where does the Spirit reside? The Church. The problems with Sola Scriptura, many of which are already under debate in Reformed circles, always point us back to the "pillar and ground of the truth" (1 Tim. 3:15), of which Christ promised the Spirit would lead us (John 16:13). Of course, this thrusts us into more complicated (and more important) debates as to how we know the true Church. The Fathers, for their part, always argue for the necessity of holiness, that is, living in the Spirit, for proper interpretation and application of the Scriptures: one must engage in the life of the Church, the eternal Life of Jesus Christ, to be a theological authority.