Yet, RDS can't scale up much. You are stuck with a fixed number of HA instances, and a fixed number of read replica. You want a cluster of twenty nodes, roll your own.
Did you ask them to increase the limit? They usually increase the limit (regardless of service) if you ask. The current limit is 40 instances and 5 read replicas per master.
This is one area I think Azure does shine... Azure's storage tables, blob and queues are dead simple and inexpensive to work with, and Azure SQL is priced better than any cloud db competitor.
Keeping hobby projects under $10-20/month is sometimes hard...