Thanks for the response, Victor. I've got ARR setup and running and I have this working fine with other sites.
I've actually discovered that this issue is caused by Sitefinity responding with a 301 (Moved Permanently) HTTP code for the page. It looks like this is occurring because the Sitefinity site has been hosted under a virtual path. When a page is requested using a URL outside of this virtual directory, Sitefinity wants to redirect to the actual path.
I had the same issue when attempting to rewrite the root site request (i.e. mysitefinitysite.com/) away from Sitefinity. This was the original impetus for placing Sitefinity in a virtual path.
For the benefit of others, I have worked around this for now by creating a separate IIS site which will sit in front of the Sitefinity site and direct traffic appropriately.
Is it possible to configure this redirect behaviour? It would be great if we could understand the circumstances that this occurs, too.