Francis,
thank you for your reply. It seems I have fixed the issue. However, I just wanted to say that in stream mode, you can use NGINX as a forward proxy as well. As you mention, in stream mode, NGINX behaves as a "TCP router" in the sense that it just relays segments or packets using the correct network interface as per routing tables. In other words, NGINX is not aware if it is proxying packets inside or outside, it is just "routing" them according to its config file and the OS IP tables (i.e., selecting the correct network interface).
Ciao,
-A.