For what it's worth, here is Richard Bauckham's take on the article:
R. Bauckham, Jesus & Eyewitnesses, pp. 194-195 wrote:It is notable that in all four Gospels this character is called "the servant of the high priest" (Matt 26:51; Mark 14:47; Luke 22:50; John 18:10). The high priest certainly had many more servants or slaves than one, and according to John 18:26 more than one such were members of the arresting party in Gethsemane. Commentators have therefore been hard pressed to explain the definite "the" in this case. Perhaps the meaning is that this servant of the high priest was the officer in charge of the arresting party. He was the most important person in that party, but his name may have been remembered in the early Jerusalem church not simply for that reason but also because of the injury to him remained, so to speak, an unsolved crime of which Peter was the as yet undetected perpetrator. Malchus was an influential person in the high priest's entourage with a personal grudge against the disciples of Jesus.
Not exactly sure what Bauckham is suggesting but perhaps having a personal grudge against Jesus made this man notorious enough to refer to him with the article? Bauckham also floats the leadership idea, but I think your argument against it is probably the stronger. At any rate, John 18:26 (which you also cited) is fairly clear that there was more than one slave in Gethsemane in at least John's mind. (The healing, though not the name, of Malchus is told in the Lukan account.)
In terms of semantics, Stéphanie Bakker proposes the following definition for the (definite) article:
Bakker, The Noun Phrase in Ancient Greek, p. 162 wrote:I therefore conclude that a definite article is appropriate if the speaker presents the referent in question as unequivocally relatable to an available cognitive structure that is relevant in a given discourse.
But I don't know how to relate this dude to a cognitive structure unless he was fairly well-known / notorious / something to first-century Christians.
Bakker's definition also has problems with two other definite nominals in Matt 26:51, Καὶ ἰδοὺ εἷς τῶν μετὰ Ἰησοῦ ἐκτείνας τὴν χεῖρα
ἀπέσπασεν τὴν μάχαιραν αὐτοῦ καὶ πατάξας τὸν δοῦλον τοῦ ἀρχιερέως ἀφεῖλεν αὐτοῦ τὸ ὠτίον
. Since people have two hands and two ears, the referent is not unequivocal because we're not told which one in either Matthew or Mark. (Perhaps the reference to the hand is OK under the assumption that it would be the dominant hand, probably the right. The detail in Luke and John that ear was the right one might suggest that he was attacked from behind or from an angle.)
Stephen C. Carlson, Ph.D. (Duke, New Testament)