Brondos on PS and Sacrifices

The part of Brondos' book Paul on the Cross which I have found most convincing and interesting so far is his case that Old Testament sacrifices were not understood to work by Penal Substitution (pp 20-30). Here are some of the arguments he gives against this idea:

1. In the Mosaic law, transgressions deserving of the death penalty are precisely those that cannot be atoned for by a sacrifice, whereas those that do not deserve the death penalty are the ones that can be. This is inconsistent with the idea that the sacrifice dies a substitutionary death.
2. Flour can be sacrificed instead of an animal if a person is too poor to afford one. It is hard to think of flour as undergoing substitutionary death.
3. In the 'peace offering' an animal is sacrificed, but there is no atonement or forgiveness taking place. So if sacrifices work by PS, then what's the point of killing this animal?
   
4. The only time sins are said to be transferred to the animal is on the day of atonement, where the goat specifically has two hands placed on it and the sins of the people prayed onto it and then is sent away alive rather than sacrificed.
5. According to PS, sacrifices should become impure as our sin is transferred to them. But they are described as "most holy" (Lev 6:29) and the priests eat the flesh.
6. There are plenty of instances of God granting forgiveness without sacrifices, and refusing it where sacrifices were given. Thus a substitutionary death appears neither a necessary nor sufficient condition for atonement and forgiveness. The bible depicts it being up to God alone whether forgiveness is granted, which he decides as he wills based on the condition of the human heart.
   
7. It was the Jewish belief that atonement and forgiveness came primarily through repentance and prayer, the sacrifices merely accompanied the prayers like the incense.
   

While Brondos' treatment of how sacrifices don't work was nice and thorough, I found him both brief and vague when it came to explaining just how sacrifices do work.

Also on the subject of sacrifice, I recently found a lengthy bibliography here of scholarly works on the meaning of sacrifices. Thank you Professor James Watts for making that available.