Essentially there are four general interpretations that are being discussed here:
(1) "Be shepherds of the church of God, which he bought with his own blood," in which HIS OWN = God's.
(2) "Be shepherds of the church of God, which he bought with his own blood," in which HIS OWN = Christ's. The interpretation here is simply that the author was being sloppy and forgot what the subject was and changed reference in mid-sentence. There was a reference to Christ in v. 24.
(3) "Be shepherds of the church of God, which he bought with the blood of His Own," in which HIS OWN = someone other than God (i.e. Jesus). This is the substantive reading, in which "HIS OWN" is used as a noun in its own right.
(4) "Be shepherds of the church of God, which he bought with the blood of his own Son," in which an original hUIOU was accidentally deleted by a copyist because it was next to a similar TOUIDIOU. This was cited by the Society, in addition to (3), as a rationale for its rendering. This would make the rendering a conjectural emendation.
For the sake of completeness, one could also suggest on less plausible grounds:
(5) "Be shepherds of the church of God, which he bought with his own blood," in which HIS OWN = the Holy Spirit. This is on the basis of the mention of the Holy Spirit and its work in the previous verse.