I'm not sure how many classes do you have that depends on Config class, so this may not help.

I think that, instead of having to pollute the namespace of your classes somehow, you should make Config an abstract class and make the the parent classes (in the top of hierarchy) to inherity it. As Perl supports multiple inheritance you shouldn't have any problem with that if you take care with the names that you're going to use for the variables. Creating them with use constant looks like a good idea too.

Of course, this will require that you change a lot of code, so you must consider if this is applicable for you.