I know I can't use 'push' because the elements of @array are references.

Huh? push doesn't care what the elements of the array are. If you want to add elements to an array, just push with the name of the array as first argument:

    push @array => @new_array;  # Adds four elements to @array
    push @array => \@new_array; # Adds one element to @array,
                                # it being a reference to @new_array.
    push @array => [@new_array];# Adds one element to @array,
                                # it being a reference to a copy of @n
+ew_array.
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Abigail