If you run the Briss PDF output through Ghostscript to generate a new PDF, I believe it will permanently get rid of the cropped-out material so that it won't come back in calibre. E.g.
gs -sDEVICE=pdfwrite -dCompatibilityLevel=1.4 -dNOPAUSE -dQUIET -dBATCH -sOutputFile=output.pdf input.pdf
(Thanks to
Andrea Lazzarotto for the tip.)