Points of contention:
-You automatically assume "God our Savior" in v. 3 is Christ. There is no textual reason to assume this. God is mentioned again in verse 5, definitely referring to the father, making distinction with the Son/Mediator.
Verse 3 does use the qualifier - God our Savior. Verse 5 establishes again for any that might be mistaken that there is one God; that there is a mediator between God and man as a separate business relegated to the Son. That only further signifies the "difference" (so to speak) of the Son (touched by our humanness). Combined with verse 6, Paul is stating there is one God, and then he is stating the mediator Christ and the work Christ accomplishes toward God. Do so by Paul supports the view that is consistent with the OT.
I believe it is dangerous to begin to assign any positive desires that Jesus is expressed to have as being different than the Father's. Jesus "willed" that Jerusalem would come to him, though they did not. It seems a stretch to thing that the Father had no such desire. I begs the question: "Was this Jesus simply expressing some human weakness of emotion? Was it a sinful desire? Was Jesus subject to such desires that were so out of step with the supposed desires of his father?
A problem happens when one would consider that different means less. That is just not a true line of reasoning.
Jesus' ability to be experienced with human frailty and weakness of the flesh is not placing him as less than God, but in the capacity of a mediator with first hand experience. He, alone, knows what it is to be fully God and yet fully human. Jesus experienced temptation and testings in all points as any human. God cannot be tempted or tested in such a manor.
One should never consider that Jesus was "less" in that He experienced the "positive desires... expressed as different from the Father's." He expressed negative desires as you pointed out and remained submitted to the desire (will) of the Father, why not the positive ones, too. That is part of his humanity. But again, different does not mean less.
***Finally, if my above 2 arguments are inadequate: JESUS IS GOD!!! If Jesus desires some thing, it by definition means God desires it!
Not at all. Again, I point you to the scene of the Garden prayer that you used as evidential. God did not desire what Jesus in the Garden desired. That did not make Jesus sinful, but reflected the humanity of the word "desire" that God does not manifest.
God has no doubt and no hand wringing hopeful anticipation that humanity enjoys (to use the extreme to prove the point). If God desires to create - it is done. If God desires to bring all Israel back into the land, it is (will) be done. If God desires one saved - that person is saved. Jesus expressed desire that God did not. That is not sinful, but a statement born out in Scriptures.
Another indication of this submission, is when Jesus was a child. He stayed back at Temple and debated with some of the members of the BB.
When questioned, He said, "I've got to be about my Father's business." This was showing the desire (will) of the Father; however, Jesus was submissive to the human parental unit and returned home. Here is an example of Jesus expressing His own desire, but also being submissive to God's will of honoring the parental unit, submitted to God's desire (command). Where some would see a conflict, the interplay of "desire" is born out in practical application by the Son.
Saying otherwise cheapens one's view of Jesus' divinity. EVEN IF such a desire is shown to be different than the Father's desire (and I'm not convinced it is)....Then it is still unbiblical to look at these verses and conclude the exact opposite of what they say: "God...DOES NOT desire that all men to be saved." You can argue about what kind of desire that is, and why all men are not saved, but denying the clear statement is not an option.
On the contrary, there is no cheapening but a greater awe that the very God (Abba - papa) can now by extension through the Son, become aware of the weakness of humanity. The Son performs what the Father wills. That is stated by Christ throughout his ministry. He even states to the Apostles, "If you have seen me, you have seen the Father."
It IS Biblical to consider that the desire (hope for, longing) that Christ experientially demonstrated is NOT the same in type as the desire of the Father. I repeat: Different does not mean less. It is clear throughout the OT that the mere "desire" of God manifests as more of an "If / Then" characteristic. In dealing with man God often uses a type of - If you do ..... Then I will do.... But such is not a part of the believer, nor appointed to the Son. The "if / then" statements are clearly mute in favor of the heir relationship to the Father. God deals with the believer through the Son and Spirit.
Here is a short list of how the difference is experientially shown between God and the Son.
God arm is not shortened (weak) nor does He sleep or doze off. Christ became bone weary, and required deep sleep.
God is unaffected by pain and discomfort. Christ suffered often, and didn't even have a pillow to comfort his head.
Christ states, "If I be lifted up I will draw all men unto me."
Is that a true statement? Certainly.
Is it the Father's desire the Son have that draw? Certainly.
Does the Father draw all men unto Him? No. There are spheres of influence and authority in which lines of demarcation establish the "desires" of the Trinity.
It is impossible for the Father to draw all men unto Him; there is no fellowship between Godly Righteousness and unrighteousness. Father is not the Redeemer/mediator, that is the work of the Son.
God "desires" (wills, appoints) salvation. The desire (will) of the Father is performed by the Son mediator through the work of the Holy Spirit (the Word and Spirit); because of the work of the Son, the believers become heirs of God, and then God is called Abba (papa). The validity of the view is also given by Paul in Ephesians 3:14-21. Paul uses an interesting play of wording to describe the final authority of all is in God
"14 For this reason I bow my knees before the Father, 15 from whom every family in heaven and on earth derives its name, 16 that He (the Father) would grant you, according to the riches of His glory, to be strengthened with power through His Spirit (the Father's Spirit) in the inner man,"
The next part shows why the Father determines this is necessary.
17 so that Christ may dwell in your hearts through faith ; and that you, being rooted and grounded in love, 18 may be able to comprehend with all the saints what is the breadth and length and height and depth, 19 and to know the love of Christ which surpasses knowledge, that you may be filled up to all the fullness of God.
Be careful reader to remember that the purpose (desire) is granted from God. Christ does the work.
"20 Now to Him who is able to do far more abundantly beyond all that we ask or think, according to the power that works within us, 21 to Him be the glory in the church and in Christ Jesus to all generations forever and ever. Amen."
Who is the "to Him" part of this passage?
Is it Christ? Some would appoint that view.
Is it the Spirit? Some might suggest that view.
Is it the Father? YES! For verse 21 clearly shows the "to Him" is the ultimate glory given both in the church and Christ.
What does that have to do with "desire"? It shows that difference does not mean less.
Sorry for the long post, and it wanted to rabbit trail, but I think I edited it enough.
Like I said, I consider this a minority view, consistent with the Scriptures, but largely ignored because human kind want a "daddy" not a God.