It would be possible to offset both of them, but I think you might be better served by approaching the problem from a different angle. You can control the relative positioning of stem and note head through 'stem-attachment, which is a property of NoteHead. The flag will move along with the stem. Also, the stem will end in the same place as an ordinary stem. Try this (the color override is useful to show the start of the stem):
Oh, that was a little too hasty of me! Note heads don't have direction, so all you need is this:
customStemAndFlag = \once \override NoteHead #'stem-attachment = #'(0.5 . 0.5)
Sorry to take the Scheme fun out of it... (if this is in fact gives you what you want!)
-David