Not to be a killjoy, but I wouldn't get your hopes up. A lot of zoos, especially the larger ones, which tend to be more bureaucratic and structured, aren't very open to letting folks behind the scenes to visit animals if there isn't a connection there - a visiting colleague from another facility, a friend or family member, etc. San Diego has some pretty extensive behind-the-scenes spaces, and much of it is built for functionality, not for visitors - not only is it not as aesthetic, obviously (I've always promised staff I won't share pics I take when I'm back there), but it's also not as safe - there are a lot fewer barriers, and it would be much easier for someone who isn't familiar with protocol or safety to put themselves in reach of something they shouldn't.
That said. There's no harm in asking, so assuming you don't have an in with anyone there, the best thing I could suggest is to write an email (or, perhaps easier, a facebook message) pleading your case, explaining your passion for hyenas, and seeing if something can be arranged. A polite ask can't hurt. Just don't be offended or upset if they say "no" and understand they've got their reasons.