Use indigenous plants rather than importing 'weeds'. Find out your local native grasses and use those instead. Lomandras are probably one type. Good to hold soil together as they apparently have shallow but strong roots. Adding drainage should also be included as would the hessian types of pervious mattings.

Google Lomandra. There are quite a few types. Easy to grow, quite a lush green, will spread in the gaps.

If the murraya and other shrubs are growing well then the area must get sun and should grow grass. If it is a high traffic area you may never be able to grow grass in the area they constantly walk on. To renovate if it is sunny and neglected - spike with a garden fork all over the compacted areas put down some fresh lose topsoil and replant or turf. The only answer if it is constantly used is to put concrete or pavers down. If you haven't watered lately, water regularly and fertilise you will be amazed if it is a running type grass. Grass likes regular water and fertiliser .

Hi Brett, this is an image from Outdoor Establishments in Sydney, one of their Mosman projects. Maybe you can ask them? I'm tipping Dianella or possibly Liriope. Leaf blade is too wide to be one of the more likely Lomandra's.