I was hoping that you might come up with some interesting and compelling reason -- some problem that can only be solved by getting your hands dirty in the muck of the symbol table. Instead, I'm seeing a description of a problem that can be solved with one more layer of hard references; a hash of hashes, for example. That, you can read about in perldsc. GrandFather is right; you just need a higher level layer of abstraction; a hash of hashes.
Your situation doesn't meet the criteria for a good reason to use symbolic references in any code that you intend to keep around on your hard drive for more than a few minutes. You've stated pretty clearly, however, that you're not open to other alternatives; you know what you want, and just needed us to show you how to do it. But as the old saying goes, "now you have two problems."
It's easy to forget that the symbol table is little more than just a special hash. All of Perl's package globals live in hashes. Perl is implemented to hide that from you most of the time, but behind the scenes, they're there. You don't usually need to fiddle with Perl's hashes when you can create your own to fiddle with instead.