I have only your result when I am in the mode "remove" state !
And if i make a sufficient large selection for take the "intersection" volume resultant
that is difficult because we don't see very well this "internal" intersection!
Advantage of your "remove" method you make only one final rectangle selection.
Maybe difficult when we have many volumes!

With my "keep" method i must make some several "external" Clicks on the volumes
but be sure that i don't take the "internal" volume.
That is easy here because we have only few volumes and surely difficult when there are many volumes.

Does we have an option for this "internal" volumes selection removing
or this "external" volumes selection keeping ?