Timber fence but short concrete posts (see pic)

I intend on removing the current 1.5m fence and replacing it with a 1.8m (paling pictured).

From what I have read the paling can only extend max 150mm beyond the rail. What can I do in order to extend the concrete posts so it can pick up the new rail I need to add?

Would a capping system work like what currently pictured or would the paling still warp?

Is there another solution.

Any help would be greatly appreciated, really struggling with this one.

I would simply fix a new post to the side of the existing one. Check it out for the rails, paling then cut back the posts later.

MC