I would like to send a one-off message to all (about 90) authenticated members
in the simplest possible way. It will be a simple text message just
drawing their attention to a new poll.

I've  looked at a couple of email modules but they seem either
overkill or buggy.
 
Did you check http://drupal.org/project/mass_contact? I've tried out recently several modules for the same purpose: finding the most simple module that just can send an email to all registered users and found that one as the most easy one.

Good luck,

Hans
www.koba.be