The gateway only needs to reach out to the licensing server and to smtp (if you've configured alerts). Everything else is inbound to the gateway.
Two troubleshooting tips - first, I'd try disabling the gateway's firewall temporarily, and second I'd try a one-nic configuration. The two nic configs are useful for bandwdith increase, but not required.
I found my problem. Both you're conditions were allready met.
The problem was that I didn't configure the Additional Host Names in the LDMG webconsole. When I did, I have 6 service leve connections. This part seems to be working as I now can connect to both the LDMG and core server.
Now for my next challenge: getting a certificate.
Thanks for your help.