Not really. Traversing tree solutions (in any order) tend to be highly-recursive. Of course, any recursive solution can be implemented as an iterative solution, but recursion tends to be more natural for this particular problem.

As for arrayrefs vs. singly-linked list, I would venture that arrayrefs use less memory and will probably be faster. But if you have a working solution and speed/memory is acceptable, you might as well keep what you have.