Accessing RDS from within a Docker container without net=host?

I'm attempting to run a webserver that uses an RDS database with EC2 inside a docker container.

I've setup the security groups so the EC2 host's role is allowed to access the RDS and if I try to access it from the host machine directly everything works correctly.

However, when I run a simple container on the host and attempt to access the RDS, it get's blocked as if the security group weren't letting it through. After a bunch of trial and error it seemed that indeed the containers requests aren't appearing to come from the EC2 host so the firewall says no.

I was able to work around this in the short-run by setting --net=host on the docker container, however this breaks a lot of great docker functionality networking functionality like being able to map ports (ie, now I need to make sure each instance of the container listens on a different port by hand).

Has anyone found a way around this? It seems like a pretty big limitation to running containers in AWS if you're actually using any AWS resources.