However, unfortunately Kerberos doesn't work for me, as the sql server is in a different domain to the one that my account is in, and there is not two-way trust between the domains (long story). Using SQL server authentication is out of the question as the authentication needs to be managed via AD for security reasons.
That said, I can connect to the server from JDBC using other tools as long as I configure them to use NLTM authentication. However I can't seem to get Tableau to do this. Simba's documentation appears to suggest that it should be possible
Are you using the server name to connect? If so, have you tried using the IP address of the MS SQL server in the format IP\INSTANCE\PORT? I've seen similar issues where changed the naming format resolved the issue.