I tend to be long-winded, but on occasion I can be concise.
As you may know, the clause marked with causal hoti "because, for the reason that" semantically explains the preceding clause, i.e. John 5:27 "He gave authority to him to render judgment because (hoti) he is the Son of Man." X has AUTHORITY because HE IS THE SON OF MAN. X is FIRSTBORN OF ALL CREATION because ALL THINGS WERE CREATED IN HIM. It is Jesus' role in creation that makes him the "firstborn of all creation".
On edit: I forgot to mention that rather than being a partitive genitive, pasés ktiseós may be treated as a genitive of subordination (cf. Basics of New Testament Syntax, pp. 54-55), along the lines of the genitive in Matthew 9:34 and Mark 15:32. There is an excellent example involving prótotokos "firstborn" in Revelation 1:5, where prótotokos is paralleled with arkhón "ruler" as a noun that lexically implies some kind of rule or authority: "Jesus Christ, who is the faithful witness, and the firstborn of the dead (prótotokos tón nekrón), and the ruler of the kings of the earth (arkhón tón basileón tés gés)". The symmetry would most naturally have both clauses as genitives of subordination, with "firstborn of the dead" indicating Jesus' preeminence in the resurrection over "the dead [ones]". Finally, we may also note that Revelation 1:5 shows some affinity with Psalm 89:27 (LXX), in which David is said to be "firstborn (prótotokos) higher than the kings of the earth (para tois basileusin tés gés)", and this is a good text of prótotokos being used without a sense of generation or origin -- as David here is being adopted through kingly anointing as God's "firstborn". Thus prótotokos is used to indicate David's preeminence over the kings of the earth. This Davidic concept may explain why prótotokos is employed as a Messianic title -- like David, Jesus is "firstborn" as king, but not just over the kings of the earth but over "all of creation". Finally, taking prótotokos as the head of a genitive of subordination also fits very well with the context of v. 16-18 where Christ has supremacy over everything, including "thrones, powers, rulers, and authorities" which are subject to him (v. 16).