Very nice find! Both texts concern a cedar with its top towering into the heavens.
There is, I believe, a deeper connection as well. The Cedar Mountains in the Gilgamesh Epic (also referred to as Mashu, the "Twins") referred to Mount Lebanon and Mount Hermon (the nearby mountain in the Anti-Lebanon range) as the location of the abode of the Annunaki gods and Ishtar (Inanna), and where there was a tunnel that led to a jeweled garden of the gods (guarded by scorpion men) where one could reach an island that has a plant that confers eternal life. This is clearly background to Ezekiel's conception of Eden. In ch. 31 we read about the " cedars in the garden of God" (v. 8), the tall cedar as " the envy of all the trees of Eden in the garden of God" (v. 9), and " the trees of Eden" as "the choicest and best of Lebanon" (v. 16). In ch. 28, we read about "Eden, the garden of God" (v. 13) as located on "the holy mountain of God" (v. 14, 16), and this garden at the holy mountain contained every type of jewel (v. 13) and divine beings like cherubim. This material thus associates Eden with a mountain in Lebanon, and note too that ch. 28 is addressed to the Phoenician king of Tyre. The Eden narrative in Genesis (J) represents a clearly independent tradition, locating Eden in northern Mesopotamia (possibly owing to Hurrian influence), but there are parallels as well; the cherubim blocking entry to the garden is reminiscent of the scorpion men in the Gilgamesh Epic and garden was construed as the place of origin of four rivers. The plain in between the Mashu mountains was the source of the Orontes and Litani rivers, Mount Hermon itself was the source of the Jordan, and Mount Lebanon was the source of the Nahr Ibrahim (formerly, the Adonis river). The Eden narrative also concerns the removal of man from the divine abode (who attempted to "become like God", resulting in divine displeasure), and this theme is shared by the cherub in ch. 28 of Ezekiel (demoted down to Sheol) and the cedar in ch. 31 (fallen down to Sheol as well). This too has connections with the Gilgamesh Epic: Mount Mashu has its peaks in the heavens (where the divine abode was located) and its slopes go down to the underworld. This tallies nicely with the concept of the cherub falling down from the holy mountain of God to Sheol. The mythological fragment in Isaiah 14 has the same theme: the morning star (v. 12) through pride attempted to set his throne "above the stars of El ... enthroned on the mountain of assembly on the utmost heights of Mount Zaphon" (v. 13) but then was cast down to Sheol (v. 15). This fits closely with what is known about Ishtar, who was closely associated with Mount Lebanon in the Gilgamesh Epic and later mythology (cf. the connection of Aphrodite and Adonis with Mount Lebanon and the Nahr Ibrahim). The consort of the Canaanite version of Ishtar, Athtart (the evening star), was Athtar (the morning star?) and in Ugaritic myth he attempted to usurp Baal's supremacy but was forcibly removed from power by Baal (who then took Athtart as his consort). The Sumerian analogue of Ishtar, Inanna, had Dumuzi as her lover, and the prominent myth about Dumuzi was his descent to the underworld. The Adonis cult similarly concerned the god's death at the Nahr Ibrahim (with ritual mourning derived from the Dumuzi/Tammuz cult). Also the sacred geography tallies well with the Gilgamesh Epic as well; the land of Bashan downward from Mount Hermon was conceptually tied to the underworld, particularly with its connection to the rephaim both in the OT and in Ugaritic myth. The Book of Watchers in 1 Enoch also draws on this mythological material as well. The fallen angels descend on Mount Hermon where they assemble and plan their rebellion. And when the archangels bind them and throw them into the underworld, they were indeed thrown into an abyss around Abel-Main downward from Mount Hermon. And the same book describes a mountain of jewels near where the tree of life is to be found.
This conception of Eden and the underworld was also relocalized to Judea. In the Ugaritic texts, El's abode was on the mountain of the heavenly council in a tent at the source of two rivers, and this is usually understood as located in Lebanon, whether at Mount Lebanon or Mount Hermon. Psalm 29 and 42 represent a similar myth, with Yahweh enthroned on Mount Hermon on top the subterranean waters. When the Jerusalem Temple was built, the architect was a Phoenician -- Hiram -- so a link with Phoenician mythology is understandable. The interior of the Temple was decorated like a garden: palm trees, flowers, pomegranates, cherubim, and stylized trees, whether as menorahs or the specific Asherah idol (removed finally by Josiah). Conceptually, we also have the same sacred geography transplanted to Mount Zion. This was the abode of Yahweh, and downward from the Temple Mount were the valleys leading down to the underworld: Gehenna (the Valley of Hinnom) and the "Valley of the Rephaim". Below the Temple Mount was a spring named Gihon, identical to the name of one of the rivers in Eden. Later Jewish legend claimed that the Temple was built on top the subterranean waters. This also explains the concept of Zion in later Jewish apocalyptic. In post-exilic prophecies in the OT, Zion flowed forth living waters to the whole earth, and in Revelation, the garden of Eden was restored at Jerusalem , with the trees of life and rivers flowing forth with living water. These ideas have a long pedigree but ultimately derive from Semitic mythologies dating as far back as Ugaritic texts and the Gilgamesh Epic.