I think you have the right idea about doing everything backwards for the opposite side. Basically, on the same row you bound off on on side, you want to match it, mirror image on the other side. It may mean binding off on the purl row. If it's impossible to do it the same row, then do it one row later (or earlier).
Yes, "with right side facing," in stockinette stitch, means the knit-side is facing, and you'll begin with a knit row.