In Writer I would like to divide the 8.5" x 11" pages into four quadrants of flowing text, with front and back printing, so that each sheet of paper yields eight 4.25" x 5.5" pages.
Are you asking about Printing Multiple Pages on One Sheet?
Might be 8 page imposition but that is print layout task, not word processing. Whole pages have to be upside down so the final can be folded and trimmed with all pages in order. See Wikipedia Imposition