@navpat Thank you for your interest in using RMI on Azure Web Apps.
You are able to do RMI over HTTP as it's a built-in functionality. Please see here for more details on that.
If you are required to use ports rather than HTTP, you can look into using an Azure Web App Container, which still only uses 80 and 443 but you can open the necessary RMI ports on the container and then map those ports to 80 and 443.
Please let us know if you have any further questions or concerns regarding this setup. If not, we would appreciate it if you could mark this reply as a verified answer.