Hi Adrian,
Wow ! that's a fair amount of lawn to deal with in one go I must say, also you've got a gorgeous garden and home design / location there.
One thing that does concern me a little bit though is that quite a bit of it must be in the shade from those trees and rock garden walls most of the day. Santa Ana Couch generally likes to have 6 hours of sun on it per day so this might be a bit of an challenge in its rapid recovery.
Maybe you could clarify this for me as I don't live there and don't know your particular daily sun situation.
As far as the actual lawn is concerned I feel it is rather thatchy and scalping it probably won't be enough as due to its age it will also require scarification which is the process of de-thatching the root system (subsurface) which is choking itself. Since you will have to do that I would delay all the work until October next year and just keep up the normal mowing at this stage to keep up the greenness on top.
BTW you'll have to either organise someone to do the scarification work for you or hire the machine to do it yourself from a say, Kennards Hire outlet etc. Scarification has to be done every few years to keep up the lawns youth. If you intend to do it yourself we can walk you through that process but it will be a good days work for the amount of lawn you have there.
Just wish we could do the same to ourselves.
Cheers,
BB.