I wouldn't be inclined to accept the interpretation that the Temple sacrificial system would be the abomination of desolation.
1. Paul declared the law to be good and holy.
2. Paul and the early church regularly engaged in Temple ritual after the resurrection.
3. Those sacrifices were a picture of the one sacrifice, so they are recommended by Hebrews to be reflected upon in a holy manner.
Sacrifices pointed forward to Christ.
Once he was sacrificed all other sacrifices became pagan.
Christ was the last and only final sacrifice God said he was sick of the smell of rams and bulls because man had abused the system similar to the indulgences of the church. Forty years of trial is very biblical. The law only pointed to the fact that we are sinful and can not keep the law and we are in need of the savior.