Did Jephthah Really Sacrifice His Daughter?

Commenting on Judges 11:30-40 the People's Bible says, "As horrible as the thought may be, we cannot rule out the possibility that Jephthah killed his own daughter. This understanding was held by the church fathers until the Middle Ages. This was also the opinion of the 1st century A.D. Jewish historian Josephus and early Jewish commentators. At the same time we may hope that a redemption was made for the daughter's life. The Lord had accepted a ram as a substitute for Isaac's life after Abraham had demonstrated that he would not withhold his son, his only son, from God (Genesis 22:13). Similarly, the firstborn of every womb belonged to the Lord but was redeemed by a setting aside of the Levites for perpetual service (Exodus 13:1,2; Numbers 3:11-13). And this raises the second possibility. Jephthah may have kept his oath by binding his only child to a life of service to the Lord that excluded marriage. This, however, would be the only instance of such a dedication in the Old Testament. The laws of Moses called for no such vow."

The Concordia Self-Study Bible seems to think he went ahead with the burnt offerings since that was what he vowed to do. The Kretzmann commentary leans the opposite way, that his daughter was able to live but not marry.

To me it's hard to believe that the sin of taking a rash vow could be made better in any way by going through with that vow. Why not immediately repent and rely on God's mercy? A couple different  passages in the Old Testament (of course for Jephthah these unfortunately came after his time) point toward God responding favorably to this course of action:

1. More than once in the Old Testament God stated "I desire mercy, not sacrifice" (1 Samuel 15:22, Hosea 6:6, also see Matthew 12:1-8), meaning that what was important to God was that his people place him as the top priority in their lives and actions rather than self-righteously following every letter of the law.
2. God states a couple times how he was disgusted with child sacrifice (Jeremiah 7:31, 32:35). While this was coupled with idol worship, which God hated, he has especially strong words for this specific act of idol worship.