I know A LOT of restaurant workers in Los Angeles (I work two restaurants myself), and I can honestly say that there is absolutely NO conflict here.
In the past, my restaurants have been as little as 5 miles apart, and there's never been an issue. If a restaurant owner wants exclusivity, then I'd insist on a 2 or 3 day per week minimum. (Thurs., Fri. & Sat.) But I've never met one who wanted exclusivity.
By the way, getting the same customers from different restaurants is a GOOD thing. You want people to ask where you are performing, and who ask the management about you when they make reservations.