The full paramiko distribution ships with a lot of good demos.
In the demos subdirectory, demo.py and interactive.py have full interactive TTY examples which would probably be overkill for your situation.
In your example above ssh_stdin acts like a standard Python file object, so ssh_stdin.write should work so long as the channel is still open.
I’ve never needed to write to stdin, but the docs suggest that a channel is closed as soon as a command exits, so using the standard stdin.write method to send a password up probably won’t work. There are lower level paramiko commands on the channel itself that give you more control – see how the SSHClient.exec_command method is implemented for all the gory details.