Yes, getting there is the problem. It is out of the way and cannot be reached by public transportation. Unlike the San Diego Zoo, which is near downtown and served by bus (and if you are in good shape, you can actually walk there from downtown, which I have done).
Good plan to stay there all day, as you will need it in a place like this. Too bad you are not going later in the summer when they stay open until early evening.
There are at least two or three San Diego people on this forum, plus a few from Los Angeles who might be able to drive down. Hopefully someone will pick up on this thread and help you out. I would do it, but I have been to southern California so much that I am trying to stay away for a couple years.
If you are interested in wolves, there is a wolf center in a scenic area of the foothills just east of the Safari Park. I have not been there, but it looks interesting.