A. Your statements about the job market makes me suspect that you are not a licensed psychologsit, which is a prerequisite to go to a psychoanalytic institution. Psychoanalytic training does not lead to licensure.
B. Based upon my own experience:
1) Psychoanalysis almost requires a private practice setting, in a wealthy area. You need patients with: some minor psych problems, an interest in an obscure treatment, the ability to cash pay for 3 sessions a week, whose work allows 6 hrs of absences every week (when you include a minimal commute), etc. These factors are no longer consistent with most other settings. And psychoanalysis is getting longer.
2) Some academic settings still value things associated with psychoanalysis (e.g., clinician with tons of publications in obscure journals, who tends to stay out of the way, and has a reputation as fancy).
3) The "job market" for psychoanalysts is basically non-existent. The academics in psychoanalysis seem to practice until much much later in life (e.g., 80s).
4) Since admissions is not really an issue for psychoanalytic institutions, I don't know why you would choose that school. The oldest and arguably most respected psychoanalytic training center, The New York Psychoanalytic Institute is close-ish. Arguably the second most respected training center, William Alanson White, is right there. Brooklyn to the upper west side is what, 30 min on the A line? And you're probably online for classes anyway. That's like drinking a flat cream soda in your fridge, when there is a corner store full of ice cold Coca-cola and Pepsi at the end of the block .