The problem I am having is that when I assign a reference to an undefined list, the modifications I make are not reflected.

Maybe I'm a little slow (wouldn't be the first time), but I can't figure out what you mean. Could you show us a small code sample?

my %stacks = (
  stack1 => [],
  stack2 => [],
);
[download]

That should do what I think you want, but it seems straightforward enough that I assume I am not understanding your question.