Refuting Christian attempts to discount Jesus' teachings using Matthew 28:16-20

Preamble
Christians employ two related strategies to discount Jesus' teaching.  I intend here to refute these attempts by looking at one particular verse in Matthew (28:20a).  That Christians discount Jesus' teachings sounds odd, but the reason for it has to do, in my opinion, with a misreading of Paul.  Since many evangelicals get Paul wrong and since this misreading of Paul conflicts with Jesus' teaching, then the teachings of Jesus must go.  It's as if Christians are given a choice between Jesus and Paul and they choose Paul.

Two Strategies to Discount Jesus' Teachings
Christians try to discount Jesus' teachings by either claiming (1) that Jesus' teaching were only for the Jews or (2) claiming that Jesus' teaching occurred before the New Covenant which commenced at his death, therefore Jesus' teachings are no longer operative.

(1) It is true that Jesus did teach mostly Jews (Matthew 10:5-6; 15:25; Romans 15:8).  However, this does not necessarily mean that his teaching does not apply to Gentiles.

(2) It is true that Jesus taught before he died, but this does not necessarily mean that his teaching is obsolete given the New Covenant.

Matthew 28:20a
This verse occurs in the passage where Jesus commissions the church (28:16-20):

Now the eleven went to Galilee, to the mountain where Jesus commanded them, and having seen him they worshiped him, but some doubted.  And Jesus approached and spoke to them saying: "All authority in heaven and on the earth has been given to me.  Go therefore and make disciples of the all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit.  Teaching them to obey all the things I have commanded you.  And behold I am with you always, to the end of the age." [italics mine]

This passage refutes in one fell swoop the two strategies to undermine Jesus' teachings.  The first thing to notice is that Jesus directs his words here to "the eleven" so when he says "all the things I have commanded you" he is meaning the disciples.  It is to his disciples that Jesus teaches in the five great discourses in Matthew (also, summaries of Jesus' mission mention teaching throughout the gospel [4:23; 9:35; 11:1]):

1. Sermon on the Mount (5-7) see 5:1.  Notice that the mount harks back to Moses and Mount Sinai.  Could it be that his mount is the the New Covenant mount, meant to put Jesus' teaching in a new period?  In this regard, see Matthew 13:52.  The transfiguration (compare Moses [Exodus 34:29] who also appeared here!) and this scene also occur on mounts.  This sounds like "New Covenant" to me.  Even the language "all that I commanded you" harks back to Moses/Old Covenant and Exodus (see for example Exodus 7:2) which again implies New Covenant!
2. Missionary Discourse (10) see 10:1, 5.
3. Parabolic Discourse (13) see 13:10, 36.
4. Church discourse (18) see 18:1
5. End Times Discourse (24-25) see 24:1, 3.

It seems likely then that Jesus in 28:16-20 is alluding to his teaching to the disciples in the body of the gospel.  This is also brought out by the past tense of commanded.  It is unlikely that he is referring to teaching after his resurrection because Matthew does not indicate there was any!

This argues against the New Covenant ploy because Jesus is assuming that his teaching is relevant to the time of the New Covenant, since he said 28:16-20 after his death.

The word "nations" in 20:19 clearly indicates that Jesus teachings are to be passed on to non-Jews as well (Jews are included too since he does not say "Gentiles").  Also, the language of having authority harks back to Daniel 7:14 where mention is made of "peoples, nations, and languages" which also refers to non-Jews.

Theological Upshot
There is simply no good reason to claim that Jesus' teachings before his death are not relevant teachings for Gentiles.  If the teachings of Jesus do not jibe with what a Christian ought to believe maybe we need to reconsider what a Christian ought to believe.  If we had to pick between Jesus and Paul would it perhaps be better to pick Jesus?