The red clock is added so that the person who missed their deadline KNOWS that they missed their deadline.
If you don't want the red-clock to show up, we could probably write a custom component to get rid of it.
If you want to discuss further, please email info-at-avoka.com.
I had a bit more of a think about this.
Actually, you can do this right now with components that we already have.
First, you'd need to set up a custom escalation process, rather than using the built-in escalations provided by User>assignTask.
This is described here:
Then, instead of deadlining the task, just get the custom escalation process to complete the task, using ProcessUtils>Force Task Completion Force Routing.
Download here: http://www.avoka.com/avoka/escomponents.shtml