Minecraft server console SSH access

Is there any way to access the console of a running Minecraft AMP instance with full interactivity (not RCON) via SSH on Linux?

I know this is fully possible via the webUi, but it would be more practical in some situations to do it directly through a remote terminal session.

No, since AMPs backend is non-interactive there is nothing to interact with in the first place. Otherwise you’d be looking at leveraging AMPs API to do things from a console.