wouldn't it make sense that they were the "fold" being referenced? Wouldn't it make sense that the "other sheep" are just non-Jews?
This is exactly correct. I believe to understand the Gospel you just have to read it like a book. The narrative of the Gospel has Jesus destroying the whole concept of a "chosen fold." Every Hebrew he spoke to fully believed that the covenent with Abraham was with them personally as well, however they had long since broke it and it never was meant to last forever anyway. The moment the first covenent was made by YHWH and Abraham it was known that eventually his decendents would fall into idolatry and general immorality (lies, cheating, conspiracy etc). That's why a messiah was always necessary because the whole narrative of the Old Testament is largely a bunch of Shakespearean tragedies. The Hebrews were like the Buffalo Bills of the late eighties early ninties. They kept getting to the big game, but in the end they always found a way to bet it all and lose. The "other sheep" are most definitely refering to the much larger class of non Hebrews.
-Sab