Is this correct - you are trying to create an FQDN rule to allow the locked-down host to access specific FQDNs on the Internet. Is this correct? If so, this should work. Your host should send the request to the internal DNS server, which will then forward the DNS request out to the Internet through the MX. At this point in time, the DNS requested will be snooped, and then should allow your client to gain access.
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