The campground at S. Coyote Trail sounds good. Do you know of any other sites that are closer/more central to the other trails? With that campground we would have a 30-60 min drive to and from the other trail heads.
Ray, the South Coyote Canyon trail campground in the Sheep Canyon is suitable only for that trail - I was making it overnight, including some socializing and hiking. It cannot be a base for other travels, too slow drive from there.
I am usually basing my stay in the campground in Palm Canyon. It is in the western end of the Borrego Springs town. In terms of comfort and convenience this is my favorite campground ever and anywhere. It has all amenities, like showers etc. And the camping sites are large and very convenient and isolated. There are a gas station and restaurants and shops in the vicinity. It can be reserved over the Internet. They have group sites, too.
But this campground is excellent only for northern and central area of Anza. If you are going to explore, extensively, the southern part of the park, then it may be too far for you to drive to the trails - around 40 mins.
I was driving far from the Palm Canyon - we even visited the Joshua Tree National Park and found a hidden and virtually unused long off-road passage through the southern end of the park. I found that even most park rangers are not aware that the passage (totally legal) exist and drivable. But it is a long drive to Joshua Tree from Palm canyon.
I hope to be there, again, next year. A very good place for late year traveling.