Thanks for taking a look at this for me. For a minute there I felt no one was listening
Can you set a menu through the "Force a menu on the checkout" option via "Hikashop->System->Configuration->Checkout" and test it again ?
Anyway, I tried what you suggested above and I am still getting "the requested page can't be found"
I just succeed to reproduce your issue but I'm having that error page when I try to go to the Final step so it don't seem to be related to the shipping method selection.
Maybe it has something to do with the "radio buttons" and it just so happens that I am using them to select a shipping option so that's why I refer to the shipping as the issue but maybe it's the button. Maybe if I was using the radio buttons for some other options it would cause that error too. Just a thought!
Thanks!