I can get to this point pretty reliably now, but when I try the method shown I'm just as likely to go from one or no corners to two yellow corners as I am to go back again the next round. I don't mess up the solved rows of the cube; things just seem to shuffle at random at this step. I get the feeling I might not be fully understanding what it means to re-orient the cube.
State 1: Y B Y G O Y B R R Y Y Y O Y G Y O Y R G B Which produced State 2: Y O R O B Y G Y B Y Y Y R Y R Y Y O B G G Rotated 90° clockwise (to match state 2 as per the guide) and produced State 3: R O O G Y Y Y G B Y Y Y G O Y Y Y R B R B
...which coincidentally solves it this time. Guess it sensed my crying out for help.
I guess what it boils down to is I'm not sure what to do when I get two corners up, as I haven't gotten particularly good at predicting where pieces will end up at this stage in the puzzle as of yet. Any advice to be offered on that point?