The answer is hinged on certain beliefs that must be taken for granted as factual. Meaning to say, that if there are sources in Chazal, they can only be as exact as other geographical locations being used as reference points. This of course excludes topographical reference points, which probably cannot be disputed.
Additionally, the source you quoted does address the its borders; "from Kfar Chananya and above - all [of the land] that does not grow sycamores - is the upper Galilee; from Kfar Chananya and below - all [of the land] that does grow sycamores - is the lower Galilee".
The modern-day Kfar Chananya is said to be not far from that of the one recalled in the Mishnah.
According to Jewish encyclopedia and Steinsaltz, Gitin 76a(2), Kfar Utnai was the bottom of the Galil. Steinsaltz also ideintifies it only several kilometers from the modern-day Ein Ganim. (See Steinsaltz for map, too.)
Quotations that reference the Galil as having certain qualities, such as the production of olives and olive oil, also confirm modern identifications.
Yerushalmi, Shabbat 16.8:
גליל גליל שנאת התורה סופך לעשות במסיקין
In modern-day old-city Tzfat, there is a sign on a wine shop which quotes this Zohar, indicating that the upper Galil is potentially at least by Tzfat.
וְאָמַר רִבִּי יִצְחָק, לֵית לָךְ חֲמַר דְּאִתְקְרֵי חֲמַר טוֹב, כְּחַמְרָא דְּאַרְעָא דְיִשְׂרָאֵל. וְיַתִּיר עַל כָּלְהוֹן, חַמְרָא דִּגְלִילָא עִילָּאָה.
Rabbi Yitzchak says: Israel has the best wine, and the best wine in Israel is in the upper-Galil.
Questions like this are even further reaching when we think of identifying the tribal portions of Israel. According to the nach, Galil is in the portion of Naphtali. And so, if we think we can identify the location of Naphtali's portion, we should also know, roughly, that of the Galil. Here is an old map. And here a new one.
וּמִמַּטֵּ֨ה נַפְתָּלִ֜י אֶת־עִ֣יר ׀ מִקְלַ֣ט הָֽרֹצֵ֗חַ אֶת־קֶ֨דֶשׁ בַּגָּלִ֤יל וְאֶת־מִגְרָשֶׁ֙הָ֙ וְאֶת־חַמֹּ֥ת דֹּאר֙ וְאֶת־מִגְרָשֶׁ֔הָ וְאֶת־קַרְתָּ֖ן וְאֶת־מִגְרָשֶׁ֑הָ עָרִ֖ים שָׁלֹֽשׁ׃
From the tribe of Naphtali, Kedesh in Galilee—the city of refuge for manslayers—with its pastures, Hammoth-dor with its pastures, and Kartan with its pastures—3 towns.
In Wars chapter 3, there is a description of the area. Although not a Chazalic source per se, it is potentially of value, considering the time of its writing.
- Now Phoenicia and Syria encompass about the Galilees, which are two, and called the Upper Galilee and the Lower. They are bounded toward the sun-setting, with the borders of the territory belonging to Ptolemais, and by Carmel; which mountain had formerly belonged to the Galileans, but now belonged to the Tyrians; to which mountain adjoins Gaba, which is called the City of Horsemen, because those horsemen that were dismissed by Herod the king dwelt therein; they are bounded on the south with Samaria and Scythopolis, as far as the river Jordan; on the east with Hippeae and Gadaris, and also with Ganlonitis, and the borders of the kingdom of Agrippa; its northern parts are hounded by Tyre, and the country of the Tyrians. As for that Galilee which is called the Lower, it, extends in length from Tiberias to Zabulon, and of the maritime places Ptolemais is its neighbor; its breadth is from the village called Xaloth, which lies in the great plain, as far as Bersabe, from which beginning also is taken the breadth of the Upper Galilee, as far as the village Baca, which divides the land of the Tyrians from it; its length is also from Meloth to Thella, a village near to Jordan.