How to restart an unresponsive TM1 Admin Server without restarting all TM1 Servers that depend on it ?

Summary

When the list of running TM1 Servers is not displayed in Architect, Perspectives, TM1 Web, or Planning Analytics Workspace, this may be caused by a TM1 Admin Server that has crashed or that is not responding despite it is "running".
This kind of error may also be found in the Event Viewer : " cannot connect to admin server at host and port 5498 "
Restarting the "IBM Cognos TM1 Admin Server x64" service is usually sufficient to solve the problem, but we can encounter two problems:

Case 1)
If the TM1 Admin Server has crashed, it is not possible to restart "IBM Cognos TM1 Admin Server x64" service. There is an error:
"The IBM Cognos TM1 Admin Server x64" service on Local Computer started and then stopped. Some services stop automatically if they are not in use by other services or programs"
This happens because one of the running TM1 Servers, after getting no response from the TM1 Admin Server, triggered the launch of a "tm1admsrv.exe" process that replaces the missing "tm1admsd.exe". This new process is then used by all TM1 Servers, and the genuine TM1 Admin Server ("tm1admsd.exe") cannot be executed because the ports (5495, 5498, 5898) are already in use.

Case 2)
If the "IBM Cognos TM1 Admin Server x64" service is in "Running" state but is not responsive for some unknown reason, then a restart should solve the problem, but restarting this service would trigger a restart of all TM1 Servers, which is something we may not want to happen, if many users are actively using a TM1 Server, or if restarting a TM1 Server is taking too much time.