Cactus, Stefano, thank you.
Aargh. It does seem to be "possible", but very difficult - it seems that a deliberate design decision was made to stop possible "hijacking" of the system console. I think that is short-sighted, but what do I know

Using the screen command does not exactly meet my needs, but it may be good enough. Pointers for others who may have the same need using PuTTY:
- To start a new screen, simply type "screen" and a new session will open.
- To exit the new session, leaving it running, simply close the Putty window
- To reattach to previous sessions, use screen -list first to list the sessions, then use screen -r <sessionname>
- To terminate the screen session, simply use "exit" or Ctrl-D at the bash prompt.