just a couple of this to try...
can you do lookups externally to the external IP address that nats to the internal IP of the GTM listner? (connectivity test)
Are you doing subdomain delegation? or host delegation?
can you do an SOA on the sub domain externally?
can you resolve the NS for the sub domain?
can you resolve the SOA for the sub domain?
set type=NS
enter domain
set type=SOA
enter domain
general rule of thumb is for delegated DNS you set a cname for the subdomain that points to NS record, client looks up hostname>returns with cname>cname lookup returns NS record>client makes a query to NS.
thanks,
B