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Moses used the term "stiff-necked" in Deuteronomy 31 which precedes the Song of Moses and the prophecy concerning the Gentiles:

For I know thy rebellion, and thy stiff neck: behold, while I am yet alive with you this day, ye have been rebellious against the LORD; and how much more after my death? - Deut 31:27

They have moved me to jealousy with [that which is] not God; they have provoked me to anger with their vanities: and I will move them to jealousy with [those which are] not a people; I will provoke them to anger with a foolish nation. – Deuteronomy 32:21

I say then, Have they stumbled that they should fall? God forbid: but [rather] through their fall salvation [is come] unto the Gentiles, for to provoke them to jealousy. – Romans 11:11

And again:

For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.

And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob: For this [is] my covenant unto them, when I shall take away their sins.

As concerning the gospel, [they are] enemies for your sakes: but as touching the election, [they are] beloved for the fathers' sakes. – Romans 11:25-28

To God be the glory, not man, never man.

Moses used the term "stiff-necked" in Deuteronomy 31 which precedes the Song of Moses and the prophecy concerning the Gentiles:

Yes, and this is super salesman Paul both reassuring the Christian converts from Judaism that their friends and relations who have not converted still have God's promise of salvation, and the pagan converts that they are just as validly saved as are the Jews - the People of God. This letter was written before the full fledged split of Christianity from Judaism - where the Jews finally got tired of this new religion kidnapping and redefining much of their religion and repudiated them completely. And, with the past 2000 years of history validating that judgement.

Please note that the concept of adopting in Gentiles is a completely NT idea and not in the OT at all. Nothing in Deuteronomy or anywhere else says that God will bring in anyone else, only that He will use the gentile nations as tools on the lives and situation of the Jewish nation. So linking Deuteronomy and Paul's epistle to the Romans is not really valid.