I suppose first the different versions in the Oral Law should be considered.
In the Tosefta Berakhot 6:23 (2nd century) it is written:
ר' יהודה אומר, שלש ברכות צריך לברך בכל יום, ברוך שלא עשני גוי, ברוך שלא עשני אשה, [ברוך] שלא עשני בור
In Yerushalmi Berakhot 9:1 (4th century) we read:
תני רבי יהודה אומר, שלשה דברים צריך אדם לומר בכל יום, ברוך שלא עשאני גוי, ברוך שלא עשאני בור, ברוך שלא עשאני אשה
Please note that the discussed blessing is not present in Bavli Berakhot 60b. However, in Bavli Menachot 43b (5th century) you can find:
תניא היה ר"מ אומר, חייב אדם לברך שלש ברכות בכל יום אלו הן, שעשאני ישראל, שלא עשאני אשה, שלא עשאני בור
The same is cited by Rosh to Berakhot 9:24 in the name of Rabbi Yehuda. In the siddur of Amram Gaon שלא עשני גוי is written, and in the available copy of Machzor Vitry the relevant part is erased, but the negative version was used.
Gra notes in his commentary on Orach Chayim the difference between the positive and the negative phrasing found in the available sources. Bach in Bayit Chadash on Tur Orach Chayim 46 gives arguments against the positive version, since the word Israelite means a free man (similar reason for ladies), therefore two blessing would be in vain, and it is not good to say less blessings.
In the negative version two wording is considered, גוי and נכרי. As you point out, the first goy is a general term in the Torah to denote a nation, while later on our sages started to denote a single non-Jewish person with this word. Isaac Satanow proposed נכרי, which was used by Heidenheim as well, but its use didn't become widespread and it's not a precise term either (see the reasons).
[I took some of the sources from My People's Prayer Book: Birkhot hashachar (morning blessings) pp. 29-30 by Lawrence A. Hoffman]