Is there a mechanism in or through iDigi to open up a remote console session with a remote X4 or X3 gateway?
Have you gone through “iDigi Web Services Programming Guide”?
By the way for your question, this link may help you for reference.
If by ‘remote console’ you mean telnet to the X4 CLI (or command line interface), that is currently not supported. It is on a request/todo list.
The X3 has no telnet/CLI.