No, I assure you that my brain does not think recursively. I have never encountered any other programmer or a math aficionado with this affliction. That makes it amazingly frustrating when people say - it is simple, just think of it as repeating a simple process until a termination condition is met. Of course I understand that and I don't usually having a problem understanding someone else's recursive solution. My problem is that my brain just doesn't think that way - I don't know how else to explain.
On the bright side, as soon as I stopped thinking about the problem thanks to your solution, I discovered how to do it iteratively using a variation on Arbitrarily Nested Loops (odometer model). If I get a chance to code it up I will but the key was to have a set of empty slots representing the combination that you copied values from as you rotate wheels on the dial. It becomes a very simple process at that point.