After re-reading your post I think I understand better why it is difficult.
however I would like to suggest it would be worthwhile effort ...
I usually only notice that I have entered the quick-filter-characters for the wrong pane
after typing a few characters and the Active pane performs the requested filter.
At this point the cursor is still in the Quick-filter-box and the Active-Pane-background turns a nice orange color (because of advanced options settings) and I realize that I want to apply the filter to the inActive pane.
Currently I have to leave the quick-filter-box, click the inactive pane to make it active and Re-Type the quick filter characters.
not all my filter's are simple
eg *smith*--NR--*__(scan)*
or *weber*--5@--*__(DL)*
so an "apply to inactive-pane button" would be welcome/best
or a history drop-down would help