Looks like the reason I couldn't find it was because someone recently rewrote the Tokyo dialect article on Wikipedia (by chance the old page was still cached and served to me!). It said, "Atashi is a feminine first person in standard Japanese, but in Shitamachi dialect, it is often used by both men and women."
Sorry if I threw anyone off by limiting it to older men. I think my brain just associates Shitamachi with older people (maybe because of this).
I also found this goo question which was answered with 「あたし」は男女問わず東京弁です。特に男が使うのが下町の特徴です。 (Forgive the translation: Tokyo-ben's atashi isn't connected to gender. In particular, it's a trait of the Shitamachi men who use it.)
Unfortunately, the Wiki wasn't well sourced, and well the goo site isn't definitive either.
By the way, I found a few links that agree with what YOU said about being used by rakugo professionals.