I think I found a solution. Completely untested.

Change

__PACKAGE__->run();
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to

# Call back run_dequeue every $seconds seconds.
__PACKAGE__->new( check_for_dequeue => $seconds )->run();
[download]

and create

sub run_dequeue {
   my ($self) = @_;
   # Can't spend long here because it blocks the entire server.
   ...
}
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