Is there a combination of columns in sys.dm_exec_sessions that is unique per the server?
Sessions belong to connections (1:M) and connections have unique GUID identifier, see sys.dm_exec_connections:


  connection_id uniqueidentifier Identifies each connection uniquely. Is
  not nullable.


Whenever you capture sys.dm_exec_sessions, join with sys.dm_exec_connections and capture the connection_id too.