After searching both 'Chaim' and 'Tajblam' under fuzzy parameters, I came up with Chaim Fajblum, who was in the right age range to ahve signed the album. In addition, if handwriting is messy it can be easy to confuse Ts and Fs, as well as As and Us.
I concluded that Tajblam and Fajblum were close enough to be a match--it is often easy to mix up Ts and Fs, as well as As and Us. Nusen (b. 1895) and Perla (b. 1900) were Chaim's parents (they lived at the same Steinmetz address), but Nusen was not deported on the same date as the other members of the family. Instead, his death date is given as July 2, 1941. Chaim, his mother, and his siblings Chana (b. 1923), Rywka (b. 1925), Abram (b. 1929), and Mojsze (b. 1931) were deported on March 1, 1942, during the month of daily deportations to Chelmno.