Exchange 2003 - Outlook RPC over HTTP fails

I'm performing a migration from Exchange 2003 to Office 365.  I therefore need to get connectivity from the Internet to the Exchange server up and running.

I've installed an SSL cert from a commercial CA, and that's working fine for Outlook Web Access.  The problem is that Outlook "RPC over HTTP" connectivity isn't working, and I think this needs to work for my upcoming migration.

I've run the Outlook connectivity test at https://testconnectivity.microsoft.com, and it fails with the following message.

Testing HTTP Authentication Methods for URL https://mail.domain.co.uk/rpc/rpcproxy.dll?mail.domain.co.uk:6002.
 	The HTTP authentication test failed.
 	 Tell me more about this issue and how to resolve it
 	
	Additional Details
 	
The Initial Anonymous HTTPS request didn't fail, but Anonymous isn't a supported authentication method for this scenario.
HTTP Response Headers:
MicrosoftOfficeWebServer: 5.0_Pub
Content-Length: 0
Content-Type: text/html
Date: Thu, 05 Mar 2015 08:55:10 GMT
Location: https://login.passport.com/ppsecure/secure.srf?lc=1033&id=1&ru=https://mail.domain.co.uk/rpc/rpcproxy.dll%3Fmail.johnston-engineering.co.uk:6002&tw=1800&fs=1&kv=1&ct=1425545710&cb=&seclog=10&ver=2.1.6000.1&rn=VPFW5mwl&tpf=94afb2ed470611f6228e012864f0dec3
Server: Microsoft-IIS/6.0
WWW-Authenticate: Passport1.4 lc=1033,id=1,tw=1800,fs=1,ru=https://mail.domain.co.uk/rpc/rpcproxy.dll%3Fmail.domain.co.uk:6002,ct=1425545710,kv=1,ver=2.1.6000.1,seclog=10,rn=X5lkRu!Y,tpf=653b54838becf5f2da5d2be65428b841
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Elapsed Time: 12844 ms.

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If I go into IIS Manager on the server, into Default Web Site, right-click on "RPC" and choose Properties, then look at the authentication methods selected for that directory, ".NET Passport authentication" is checked, "Enable anonymous access" is unchecked, and all other methods (Integrated Windows authentication, Digest authentication, and Basic authentication) are unchecked and grayed out.

How can I get this working, please?  I just need it to work long enough to migrate the data out!