Okay, so the iteration function for e^z-1 might have a radius of convergence limited by complex singularities (since it seems obvious to me that it shouldn't have any real singularities). I haven't given much thought yet to complex hyperexponents. I don't see a reason that the work I've done so far can't be extended, now that I have a power series for the iteration function. So long as it has non-zero radius of convergence, I can test it out with complex iterations and see what happens...

~ Jay Daniel Fox