I have a set-up running on Amazon cloud with a couple of EC2 Instances running through a load balancer.
It is important that the site has a unique(static) IP or set
You could use as already mentioned loadbalancer.org appliance in AWS. It would replace the AWS NAT instance and give greater functionality and include both Layer4 and Layer7, along with SSL termination and a WAF.
Best of all you get free support in your 30 day trial in AWS to help you get up and running.
Yes I am biased as I work for loadbalancer.org however I would say nothing ventured nothing gained.
This is an old question, but things have changed now.
Now you can create a Network ELB to get a LB with a static IP.
from https://docs.aws.amazon.com/elasticloadbalancing/latest/network/introduction.html
https://aws.amazon.com/blogs/aws/new-network-load-balancer-effortless-scaling-to-millions-of-requests-per-second/