I've been through on a number of oocassions although none have been a north /south route. I've been south to SAM and then west and returned the same way and its not been a problem. All I can suggest is that you ask, if they are busy you might have to stay outside their zone. I would guess that the higher you are , perhaps the better the chance.
An alternative, although I've not actually tried this myself, is to fly a DME arc around the zone.
you've not mentioned whether it would be a VFR or IFR zone transit. persoanlly find naviagting via the VOR a lot easier. IF you are lucky, they might vector you around.
just give it a go and hafve a back up plan in case they can't offer you a transit , say perhaps via Goodwood VOR?