After reading this part:
In a note below I made the point that
websites geared largely toward the
elderly, mentally challenged, or very
young can become confusing for people
when they are asked to perform a
secure password recovery routine.
Though we may find it simple and
mundane in those cases some users need
the extra assistance of either having
a service tech help them into the
system or having it emailed/displayed
directly to them.
In such systems the attrition rate
from these demographics could hobble
the application if users were not
given this level of access assistance,
so please answer with such a setup in
mind.
I'm left wondering if any of these requirements mandate a retrievable password system. For instance:
Aunt Mabel calls up and says "Your internet program isn't working, I don't know my password". "OK" says the customer service drone "let me check a few details and then I'll give you a new password. When you next log in it will ask you if you want to keep that password or change it to something you can remember more easily."
Then the system is set up to know when a password reset has happened and display a "would you like to keep the new password or choose a new one" message.
How is this worse for the less PC-literate than being told their old password? And while the customer service person can get up to mischief, the database itself is much more secure in case it is breached.
Comment what's bad on my suggestion and I'll suggest a solution that actually does what you initially wanted.