TableView with two instances of NSFetchedResultsController

After days of research and re-coding I am pretty much stumped. My goal is to get a test app running with a single tableview populated from two separate fetchedResultControllers.

I have a series of items on a shopping list, each with a department and a boolean 'collected' flag. Uncollected items should be listed by department, followed by a single section containing all collected items (regardless of department). As a user checks off uncollected items, they should move down to the 'collected' section. If s/he un-checks a collected item, it should move back into its correct department.

To achieve the first part (uncollected items), I set up a simple fetchedResultsController that fetches all items where collected = NO, and sectioned the results by department:

- (NSFetchedResultsController *)firstFRC {
    // Set up the fetched results controller if needed.
    if (firstFRC == nil) {

        // Create the fetch request for the entity.
        NSFetchRequest *fetchRequest = [[NSFetchRequest alloc] init];

        // fetch items
        NSEntityDescription *entity = [NSEntityDescription entityForName:@"Item" inManagedObjectContext:managedObjectContext];
        [fetchRequest setEntity:entity];

        // only if uncollected
        NSPredicate *predicate = [NSPredicate predicateWithFormat:@"(collected = NO)"];
        [fetchRequest setPredicate:predicate];

        // sort by name
        NSSortDescriptor *sortDescriptor = [[NSSortDescriptor alloc] initWithKey:@"name" ascending:YES];
        NSArray *sortDescriptors = [[NSArray alloc] initWithObjects:sortDescriptor, nil];

        [fetchRequest setSortDescriptors:sortDescriptors];

        // fetch results, sectioned by department
        NSFetchedResultsController *aFetchedResultsController = [[NSFetchedResultsController alloc] initWithFetchRequest:fetchRequest managedObjectContext:managedObje