Some ideas I'm working on:
Aelfric is influenced by Genesis A, which may come from Aethelwold's school (the manuscript, not necessarily the texts), sometime between 960-987. Later Aelfric begins to differ from Aethelwold on some of the details, becoming more Augustinian.

Further, why did Aelfric write the Life of Aethelwold? Unverified and unchecked theory: after his Letter to the Monks and other texts in which he differs from Aethelwold, perhaps there was political need to reiterate his relationship with that school and tradition.