The Centurion Way extension is now open and takes you further towards West Dean. It's not a sealed surface, but it is broad and well-drained so easy to cycle.
Unfortunately, the top of the extension ends in a cul de sac with no way to get to get beyond it.
When we tried it out, we took a tip from a local and backtracked a bit to a gate across a path that leads out to the A286. The gate has a padlock, but it wasn't locked. Instead, the gate was secured by a piece of rope obviously designed to allow people to get through the gate easily. The map above shows where the path meets the A286. This is a picture of the gate from the A286:
Mike Ashton has spoken to his SDNPA contact and confirmed there is no public right of way along the 15 metre, or so, long path linking the extension with the A286.
Taking a group up the extension is, in any case, a bit of a risk because - if the gate is locked - it's a long way to backtrack. On the other hand, if you're going south, you can check the state of the gate right at the outset.