Elastic Beanstalk allows you to use custom AMI, which you can customize to your liking: http://docs.aws.amazon.com/elasticbeanstalk/latest/dg/using-features.customenv.html
You can also customize many of the parameters of the non-legacy containers, even on Windows: http://docs.aws.amazon.com/elasticbeanstalk/latest/dg/customize-containers-windows-ec2.html
It is probably best to use Elastic Beanstalk, if you are already using it, as it has better integration to EC2 and other AWS resources. It is probably less likely that an MS tool will have the same level of support.