This does not answer your question, but I would argue that especially if you want to spend your career focused on psychodynamic psychiatry, you should attend a residency program that is not focused on that. psychiatry residency should give your foundation to seeing patients with a wide variety of different mental status, across the lifespan, and from diverse socioeconomic and cultural backgrounds. You really want to get solid training in neurobiological, psychopharmacological, cognitive-behavioral, systemic, cultural, and narrative based approaches to psychopathology. Psychoanalytic training is in addition to psychiatry residency, and contrary to popular belief, even back in the day where psychiatry residency was mor heavily dynamically oriented, only a minority of psychiatrists worked analytically with patients. If all you have is a hammer, everything looks like a nail. Psychoanalysis has reached the point where it does integrate different theoretical perspectives (e.g. feminist, poststructuralist, postcolonial, neuroscience based, relational) and a good psychoanalytic psychiatrist will know when to consider a neurological cause for the patient's maladies, how to appropriately use medications, when not to treat primarily with a dynamically oriented approach, and when to integrate behavioral and other modalities into treatment. The worst analysts are the ones that are dogmatic and clueless about all this other stuff.
That said you should be looking at a place that will support you taking the analytic training from your 3rd year should you wish. One of the advantages of doing your analytic training during residency training is you get some free supervision. However it is unlikely you will be able to see patients for psychoanalysis proper during residency training, but you do want to have some patients you are seeing 2x week for psychoanalytic therapy.
Another thing to bear in mind is every analytic institute has its own flavor. Chicago is much more heavily influenced by self-psychology that probably any other analytic institute in the country.