This looks like a fine book:
First Bible of the Church: a Plea for the Septuagint - Mogens Muller.
Muller apparently tries to argue his point from a Jewish perspective. There is, I believe, a great need in both Christian and Jewish circles to integrate the LXX. For Jews, the Septuagint is part of their history, a product of their religious experience. For Christians, the Septuagint is the textual foundation for their religious experience. Although, inclusion of the Psalms of Solomon is contentious point. The Psalms of Solomon are found in some lists and occasionally included in some copies of the Septuagint, however, they are not without controversy. The presentation of a pre-Christian concept of Messiah may or may not be somewhat difficult to reconcile with after two thousand years of doctrinal development.