Here's my understanding so far:
OT saints were part of many nations under many names. Chosen people were never citizens of a "chosen nation" until Christ and the nation in Christ. The chosen people of the OT were never citizens of a chosen nation.
There are no passages in the Christian Bible that talk about a chosen "nation of Israel", only a chosen people from across many nations, and it is explicitly stated that not all people of Israel were chosen. The Bible even has a passage in Exodus that alludes to the fact that Israel never became a chosen nation because they failed to be perfect under the Law.
The concept that the "nation of Israel is chosen" is not consistent with Christian scripture and is in fact from Talmudic Judaism. If you were a Talmudic Jew, that's just part of your faith. But as a Christian, it is contrary to scripture to accept the premise that a Christless Israel would have been a chosen nation, even if it contained a percentage of the population that were chosen people.