I think you can sum up what Prov. 16:4 is teaching by saying that God had express purpose in creation. He created "for his own ends" or for His own pleasure (Revelation 4:11) and for His glory (Isaiah 43:7). All of creation is thus an expression of his will and his power.
God "works all things after the counsel of his will" (Ephesians 1:11). This "all things" includes the fall of sparrows (Matthew 10:29), the rolling of dice (Proverbs 16:33), the slaughter of his people (Psalm 44:11), the decisions of kings (Proverbs 21:1), the failing of sight (Exodus 4:11), the sickness of children (2 Samuel 12:15), the loss and gain of money (1 Samuel 2:7), the suffering of saints (1 Peter 4:19), the completion of travel plans (James 4:15), the persecution of Christians (Hebrews 12:4-7), the repentance of souls (2 Timothy 2:25), the gift of faith (Philippians 1:29), the pursuit of holiness (Philippians 3:12-13), the growth of believers (Hebrews 6:3), the giving of life and the taking in death (1 Samuel 2:6), and the crucifixion of his Son (Acts 4:27-28).
From the smallest thing to the greatest thing, good and evil, happy and sad, pagan and Christian, pain and pleasure - God governs them all for his wise and just and good purposes (Isaiah 46:10). Lest we miss the point, the Bible speaks most clearly to this in the most painful situations. Amos asks, in time of disaster, "If a calamity occurs in a city has not the LORD done it?" (Amos 3:6). After losing all ten of his children in the collapse of his son's house, Job says, "The LORD gave and the LORD has taken away. Blessed be the name of the LORD" (Job 1:21). After being covered with boils he says, "Shall we indeed accept good from God and not accept adversity?" (Job 2:10).
Oh, yes, Satan is real and active and involved in this world of woe! In fact Job 2:7 says, "Satan went out from the presence of the LORD and smote Job with sore boils from the sole of his foot to the crown of his head." Satan struck him. But Job did not get comfort from looking at secondary causes. He got comfort from looking at the ultimate cause. "Shall we not accept adversity from God?" And the author of the book agrees with Job when he says that Job's brothers and sisters "consoled him and comforted him for all the adversities that the LORD had brought on him" (Job 42:11). Then James underlines God's purposeful goodness in Job's misery: "You have heard of the endurance of Job and have seen the outcome of the Lord's dealings, that the Lord is full of compassion and is merciful" (James 5:11). Job himself concludes in prayer: "I know that You can do all things, and that no purpose of Yours can be thwarted" (Job 42:2). Yes, Satan is real, and he is terrible - and he is on a leash.
As for the alternative views you are considering, they cannot consistently say that God foreknew who would be saved and then preach that God is trying to save every man. Surely if God knows whom He can save or who will be saved, then who would say that He is trying to save more? Certainly, it is foolish to assert that God is trying to do something which He knew never could be accomplished.
Likewise other positions cannot consistently say that God foreknew which sinners would be lost and then say it is not within God's will to allow these sinners to be lost. Why did He create them? Let the Synergist consider that question. God could have just as easily refrained from creating those that He knew would go to Hell. He knew where they were going before He created them. Since He went ahead and created them with full knowledge that they would be lost, it is evidently within God's providence that some sinners be lost, He evidently has some purpose in it which we human beings cannot fully discern. The Christian humanist can complain against the truth that God chose to allow some men a final destiny of Hell all they want, but it is as much a problem for them as for anyone. As a matter of fact, it is a problem which they must face like anyone else. If they face it, he will have to admit either the error of his theology or deny foreknowledge all together. But he might say that God had to create those that perish, even against His will. This would make God subject to Fate.
Likewise these cannot consistently say that God foreknew who would be saved and then preach that God the Holy Spirit does all He can do to save every man in the world. The Holy Spirit would be wasting time and effort to endeavor to convert a man who He knew from the beginning would go to Hell. You hear these other positions talk about how the Spirit tries to get men to be saved and if they don't yield to him they will "cross the line" and offend the Spirit so that He will never try to save them again. Bottom line, the Synergist makes a finite creature out of the Divine Godhead.
Hope this helps clarify some things ...most of all, I would challenge you to let the conclusions you ultimately draw take into account all biblical evidence.