Update: My agency processed the paperwork submitted my the Osan Civilian Personnel Office for post allowance (PA). They are recognizing Tim as my dependent, at least for PA and living quarters allowance (LQA) ceiling. This is all more symbolic than anything, in my circumstances. The PA increased by $21 per pay period. And for my housing, I was not spending the full LQA anyway (we are reimbursed for actual expenses, up to a cap, dependent on your GS level).
But Tim is still without SOFA status. So he has to leave Korea every 90 days to re-set his tourist visa.
Well, for now I'm glad for the small step forward.