Hi Dom,
This is possible with customizations.
What you could do is create a custom field to specify the time (as, perhaps, a pick-list of pre-defined values) and then write a custom workflow rule in which any time this custom value is changed, to update/reschedule the respective object's Start Date value. To update the Start Date, you would need to construct a new DateTime object using the hours and minutes specified in your custom time field.
We are actually working on a similar app for this and will update this thread once we have it written.
Thanks!
Rob