I found out, after too many failed download attempts for no reason I could ascertain (come on, Amazon), the 1940 Census data is also available on Ancestry.com. Their servers actually served the data correctly. And so, I found this:
The apartment numbers aren't listed, and the building added an apartment to my entrance sometime in the last 70 years, but I think I can work it out. The first column shows the rent for each apartment. The three higher-rent apartments have to be the larger ones to the west. That means mine is either one of the two $65 apartments on the table or was vacant on 1 April 1940.
So the best I can do is that the three apartments on my side of the stairs that existed in 1940 contained a 35-year-old divorcée from Illinois who worked as an office manager in a brokerage, and a 64-year-old broker/solicitor from Nebraska who lived with his 84-year-old mother. My neighbors included a 51-year-old mother who lived with her 29- and 23-year-old sons, both of whom worked as wholesale salesmen; the 57-year-old treasurer of a wholesale varnish company and his 53-year-old wife; the 46-year-old head of the complaints department at Illinois Bell and his 39-year-old wife; and the building engineer and his wife, both of whom were 49.
All of these people were white, professional, and at least high-school educated. Six of eleven had college educations, a significantly higher proportion than the general public at the time. There were no children in the tier. All but two were U.S.-born. (The varnish-company treasurer came from the Republic of Ireland; his wife was English-Canadian.) All but the divorcée had lived in the same apartment for at least 5 years. Seven of eleven worked at least 40 hours during the previous week, including the poor janitor who worked 70. Salaries ranged from $600 (the 29-year-old son who sold furniture wholesale) to $5000+ (the Irish varnish company treasurer). Mrs. G.R. Walker, the most likely candidate for my predecessor in this apartment, made $2000, somewhat higher than the U.S. average salary in 1940 and approximately eqivalent to $32,000 today.
Today we're entirely professional (including three attorneys and two professional musicians), with a handful of young children, all of us college-educated or better. There is one foreign-born person; our average age, not counting the children, is about 38; and none of us worked 70 hours last week. Two of the seven apartments are rentals, the rest are owned. Adjusting for inflation, they cost almost exactly the same as in 1940.
In other words, the people who lived in my apartment building 70 years ago looked a lot like the people who live here today. And I wish I could meet them.