Using "Relative" will always lead to the total of 100%, so in won't be useful in your case.
Instead, calculate the % manually, using keyword ALL - it means ignoring chart dimensions and user selections:
Sum([Duration In Minutes])/Sum( ALL [Duration In Minutes])
If you need a more granular definition of what selections to respect and what selections to ignore, then you'll need to replace ALL with a corresponding Set Analysis condition.
Actually, what I ended up doing that got me what I really needed was modified the load script to include:
LOAD "Effective Date",
sum("Duration In Minutes") as [Daily Total Duration]Resident MetricHist
Group By "Effective Date";
Then I modified my expression to
=sum([Duration In Minutes])/sum([Daily Total Duration])
Now when I select a job, the percentage remains unchanged. If I selected a job before it would change from the actual percentage to 100%.