I find what you call "The Big Scheme" to include the "other sheep who are not of the Abrahamic fold".
IOW those in the antipathy of the Mediterranean embrace who lived way before the Genesis concept of mankind.
In the real 'Big Scheme' those 'other sheep', in the words of Christ "must also be brought in".
First we're All people.
Then Gods People, (distinguished...Hebrews, Tribes)...excluded Gentiles as a whole.
Then Gods people straying...following traditions of Gentiles.
Then Again an Offering to all People.
Hebrew/Tribes/Jews AND Gentiles...
It has always been an individuals choice...whether or not, by race they were Hebrew/Tribe/ or Gentile.
Jesus Expressly revealed...no exclusion...INDIVIDUALS...all individuals...
HAVE Option to choose. God...or God and the Christ the Lord God.
First Jews promoted Jesus' plan...that faltered and they resumed OT following (NOT all Jews...its INDIVIDUAL).
The Gentiles "primarily" Latched on ... TO The Hebrew God, His Word Jesus and His Power and Wisdom Christ. Again not all Gentiles, Individual choice.
OT fathers in Faith...are secure in God.
NT Jews accepting Jesus...are secure in God.
Droves of accepting Gentiles are ...secure in God.
The "other sheep" are "Gods people" not yet accepting Christ Jesus who was Revealed to them, 2000 + years ago.
Gentiles who accepted God AND Christ Jesus-
were NOT Appointed to teach The Tribes...nor have they...God shall send Tribal men to teach the Tribes, at the first part of the Tribulation, overlapping into mid-Trib....whereby those "other sheep" ...will become "sheep" IN Christ and Saved.