What is the best way to have a task escalation trigger a email? Our

I think your suggestion to use a ‘send message event’ to trigger a process that sends out the e-mail is the best approach to address your use case. Moreover, you can re-use the process model created to send the e-mail across different process models in your application.

If you want to keep everything in the same process model, you could use a intermediate timer event to trigger an exception flow to send the e-mail and then have the flow back into the task to issue a new task instance. Depending on how many escalations you need, this approach could clutter your process models though.