I'm confused about what the issue is. We have a number of SM configured in different datacentres. In one of the DCs we have what you are trying to configure (I think).
We have an external FW (Hardware) which has a number of external facing public IP addresses. These addresses are then routed using NAT'ing to internal IP. This all works fine as long at the specified internal IP address is configured on the SM Mail Server box along with the correct internal DNS obviously.
The above is pretty straightforward. This would be the approach for an internal only mail server too, without the external FW routing.
The part that I am confused by is
"For example, the external 69.69.69.69 is mapped to the internal 10.10.10.10. In SM (v11), I am unable to enter the IP addresses in the "bindings" area. Instead, I can only choose from the IPs SM sees on the box; these are all INternal."
That is correct, you can only choose from IP addresses allocated to that box. So, you would choose the internal IP address that is routed to your external one. If this is not working then I can only think there is an issue with the DNS/NAT'ing.