bullmastiff - leash training

Our new puppy is a 14 week old bullmastiff - he is basically a very
good puppy - perfectly crate trained, almost housebroken (one accident
yesterday), responds to "NO," no excessive barking / whining, etc. We
live in an urban area and he must go out on a leash (there is no yard).
Our biggest problem with this puppy is that he does not seem to want
to leave the apartment and will not walk on a leash. He will not walk
out the apartment door, or in the hallways or outside on the sidewalk -
he will cooperate a little better once his place to relieve himself is
in sight. He walks on the leash just about perfectly when he knows we
are heading back to the apartment. We have tried the gentle
encouragement, luring with treats, tapping the floor, lifting by the
harness and pulling along, walking ahead and telling him to come...
Nothing is working. Has anyone had a problem with this "mule"-like
behavior? The techniques in the books aren't working!!