Instead of having the engine rebuilt and having to find a shop and machinist that is reputable, why don't you have a preassembled crate engine installed. Ford Racing Performance Parts has complete brand new engines available sitting on a crate. The price for these engines is quite reasonable. You may come out ahead with an engine that is factory fresh.
You can purchase a long block and place your original intake manifold and exhaust plus the accessories to the new engine without any problem. You'll be able to keep the original look and have a brand new engine.
Ford Racing has several dealers in the Los Angeles area. Their full catalog and list of dealers is here:
www.fordracingparts.com
I would also suggest contacting the Mustang Club of America's Los Angeles Chapter for assistance in the body and restoration work.