You really want a default VPC for my existing EC2 account. Is that possible?

Yes, however, we can only enable an existing account for a default VPC if you have no EC2-Classic resources for that account in that region. Additionally, you must terminate all non-VPC provisioned Elastic Load Balancers, Amazon RDS, Amazon ElastiCache, and Amazon Redshift resources in that region. After your account has been configured for a default VPC, all future resource launches, including instances launched via Auto Scaling, will be placed in your default VPC. To request your existing account be setup with a default VPC, contact AWS Support. We will review your request and your existing AWS services and EC2-Classic presence to determine if you are eligible for a default VPC.