Basically it sounds like IaaS is fine (even though someone else manages the hardware and restricts OS choices), and even PaaS is fine (even though someone else

Basically it sounds like IaaS is fine (even though someone else manages the hardware and restricts OS choices), and even PaaS is fine (even though someone else manages the hardware, the OS, and the configuration of interpreters such as php / node.js / python / etc.), since these let you run your own code (which can include your instance of community code). Only SaaS would be excluded, as these don't let you run your own code.