According to the docs, a navigation drawer doesn't sound appropriate. It's more targeted at getting around between different activities/screens.
The View Control dropdown doesn't seem to fit either; you're not really changing views/accounts or anything, just reorganizing what's already there.
If I were you, I'd change the sort settings ActionBar item to open a dialog instead of a dropdown. You could have your checkboxes there, and a spinner for which field to sort by.