Is Melchizedek "a true Deity"? Hebrews 7:3

Jerome H. Neyrey, S.J.[1] understands the affirmations concerning Melchizedek found in Hebrews 7:3 as identifiers of "a true Deity" borrowed from "Hellenistic God-Talk".  A true deity is distinguished in several Hellenistic authors from a deified mortal by being eternal; no beginning, no generation, no birth, no death, no end. Neyrey[1] presents the evidence from the Hellenistic authors in English so there is no point in repeating it here. Neyrey argues that the language of Heb 7:3 is unmistakably a definition true deity according to Greek and Hellenistic philosophy: 

1. By examining in great detail the Hellenistic parallels to the statements made in Heb 7:3, this study has shown that the language originates in and reflects the mode of thought found in Greek and Hellenistic philosophical speculation about a true deity. Unmistakably, the author of Hebrews intends his readers to understand the figure described in 7:3 as a true deity, completely in accord with the topoi which describe true gods as fully eternal, uncreated or ungenerated in the past and imperishable in the future. —   Neyrey[1]

Heb. 7:3 ἀπάτωρ ἀμήτωρ ἀγενεαλόγητος, μήτε ἀρχὴν ἡμερῶν μήτε ζωῆς τέλος ἔχων, ἀφωμοιωμένος δὲ τῷ υἱῷ τοῦ θεοῦ, μένει ἱερεὺς εἰς τὸ διηνεκές.

Heb. 7:3 Without father, without mother, without genealogy, having neither beginning of days nor end of life, but resembling the Son of God, he remains a priest forever. — NRSV

The three alpha privatives ἀπάτωρ ἀμήτωρ ἀγενεαλόγητος "without father, without mother, without genealogy" followed by μήτε ἀρχὴν ἡμερῶν μήτε ζωῆς τέλος ἔχων "having neither beginning of days nor end of life" is a formula statement for "true Deity" according to Neyrey, well documented from primary sources in his article. R. Bauckham[2] cites Neyrey favorably in his discussion of Heb. 7:3 and divine identity. Koester 2001:348[3] suggests that the three alpha privatives ἀπάτωρ ἀμήτωρ ἀγενεαλόγητος taken alone might have been used to discredit Melchizedek, suggesting that he had no known father and mother but the following qualification "having neither beginning of days nor end of life" makes it clear that Hebrews is speaking of divinity.

Then how we avoid the obvious? That according to Hebrews Melchizedek is a "a true Deity"? Bauckham[2] claims that the author of Hebrew's had little interest in the historical Melchizedek and that we need not take Hebrews seriously as statement about the Melchizedek of Genesis 14. According to Bauckham, Koester, Ellingworth[4], Hebrews uses an argument from silence. In Genesis 14 Melchizedek arrives without announcement other than he is the King/Priest of Salem and then disappears without a trace. According to Bauckham[2] this lack of historical information is sufficient justification according to the literary customs of (late) Second Temple Judaism to fabricate a imaginary (mythical?) "textual" Melchizedek which has little or no relationship to the historical Melchizedek. This "textual" Melchizedek is made a type of Jesus Christ as High Priest using Psalm 110:4. This sounds to me a lot like the arguments used to dispose of troublesome historical figures in NT epistles like Adam for example in Paul's epistles.
      

[1] Jerome H. Neyrey, S.J. "Without Beginning of Days or End of Life" (Heb 7:3): Topos for a True Deity" CBQ 53 (1991) 439-55.

[2] Richard Bauckham, Jesus and the God of Israel p. 246-47

[3] Craig R. Koester. Hebrews: A New Translation with Introduction and Commentary. Anchor Bible 36. New York: Doubleday, 2001

[4] Paul Ellingworth. Hebrews: A Commentary on the Greek Text.