I am having exactly the same issues as Chris (user id 'cpaschen'), and on exactly the same host (BlueHost).
Refer to his post: #21988 – Restore looping after pre-installation checklist
As mentioned, I am getting exactly the same issues in the same way.
I too am using Using Kickstart PRO 4.0.0, although I am using Akeeba backup pro 4.1.2, though this will not make a difference.
Could you put me in touch with Chris to ask has his issue been resolved, and how? There is no update on the Akeeba site tickets.
I had hoped to avoid you having to spend/waste time on what is both a duplicate issue, and one which I think is associated with the host rather than Akeeba, so apologies in advance for my posting this ticket..... I couldnt find another way of making contact.
thanks,
Mike