The first question to ask is what type of irrigation is being used currently on the hedge. Most landscape oak root fungus problems are due to overwatering in summer months. However, Thuja orientalis (=Platycladus orientalis) is quite susceptible to Armillaria even without heavy irrigation as highly susceptible species do not require excessively high soil moisture to be killed.
Prior to any new planting, as much of the old hedge (including roots) should be removed. In addition, any other decaying wood should be removed. Replanting with plants that do not require supplemental watering is best. Some CA natives that make good hedges include: ceanothus, island mountain mahogany, manzanita, and toyon. Non-native possibilities include Leyland cypress and Japanese privet. Keep in mind though that even plant species listed as resistant to oak root fungus will die if overwatered.
