I had not found this answer before while searching, but found it after I posted: Default Filter Selection
I understand what Mark did in that response and it's pretty clever. My end users would prefer to have the real quarter value shown instead of the value of "Current Quarter." I have tried using this calculated filter as only the filter itself and using the real fiscal quarter value as the display for the sheets. It requires me to put he calculated filter on the level of detail shelf, which leads me to lose the line graph in the PDP Metrics Past page, which is not desirable.
I'd love to have the capability to use Tableau's built in relative date filters because that filter would do the trick for me by selecting the "current quarter" option, but we don't yet have a way to embed custom fiscal calendars in Tableau at this time.
I'm still looking for workaround soltuions similar to what Mark brought up.