No easy way ; the problem is that the initial "Save" is just triggering the process, which has not necessarily executed when the screen is redrawn (but has finished by the time that you manually "Refresh").
I have heard of solutions auto-refreshing screens but never seen them in action ; I don't think it was simple though, people messing about with javascript in the browser to make it work.
I personally use the TIP : How To Put Any Dynamically Generated Value On A Clarity Object technique to display derived information pulled from the audit tables (like status change dates which I think is what you are still trying to do) - i.e. not waiting for a background process to update data back on the object itself, just derive the data from audit, but there are still some limitations with that trick (so perhaps you could combine that 'tip' technique with the process-solution if it was REALLY important that you saw that information 'immediately').