Given that turning an active call stack into a serializable form is such a rare feature even in functional languages, iteration with an explicit stack ends up as the only practical choice for this use case.

(Also, for this particular problem, we can implement a much simpler iterative routine: create an explicit stack of forests, initially containing the initial forest. While the stack is not empty, pop a forest: if it is not nil, push its tail, then if its head tree is not empty, accumulate the value and push the sub-forest. If you're starting with a tree, then stick it in a synthetic forest. This all comes out to ~15 LOC, with no mutability except for the accumulator and stack.)

This seems like a lot of work when you could just increase the stack size instead.