αὐτοῦ versus ἑαυτοῦ in Luke’s Gospel

I am now fully annoyed by the recurring variant in the gospel of Luke between αὐτοῦ and ἑαυτοῦ.  The UBS and RP texts alternate sides back and forth.

The latest is Luke 15:5, ἐπὶ τοὺς ὤμους ἑαυτοῦ (BYZ) or ἐπὶ τοὺς ὤμους αὐτοῦ (UBS).  He places it upon his shoulders.  The KJV does not render this “his OWN shoulders” as do some recent translations of the BYZ text.  There is no real reason to.

15:26 πατέρα ἑαυτοῦ v. πατέρα αὐτοῦ (BYZ)
Again, there is no reason to render this “his OWN father.”

14:27 σταυρὸν ἑαυτοῦ (UBS) v. σταυρὸν αὐτοῦ (BYZ)
His OWN cross v his cross, this one may be meaningful.

15:20 πατέρα ἑαυτοῦ (UBS) vs πατέρα αὐτοῦ (BYZ)

Complicating this, and perhaps explaining the rise of this, is the contraction of ἑαυτοῦ which is αὑτοῦ. Note the rough breathing mark, which is the only thing that distinguishes it from αὐτοῦ.  The early papyri and uncials may not show this, so they could read either way.