Well, I did something like that. I didn't visited Irkutsk, I just got to Ulan Ude and run out of time and flew back to Moscow. Birobidzhan is at a short distance of Khabarovsk, either by train or by car, so is a good idea yours. Also, Komsomolsk na Amure is, possibly, the best city of the BAM. You can try (in April it might work) to go to the end of the BAM (Sovetskaya Gavan) and try to catch a ferry to Sakhalin Island. I tried but it was frozen. A friend from Belarus walked the 9km between Sakhalin and Russia on the frozen ocean, but he had the permit of the army, plus a sat phone, and good navigation equipment. I wanted to join him, but I wasn't fit for that activity and I felt it was too risky. Now, if I was there, i'd certainly walk it...