Searching at SVAR for Anders B?ckström 1866-1868 gives an Anders Johan Backström in the census for 1890, which would just barely fit with his emigration. He is single, born in Säter, Kopparberg in 1866, living in Borlänge (Stora Tuna) working as a "lokeldare" which might fit with Andrew being a labourer at a Pullman shop.
Unfortunately his date of birth seems to be January 31, not June 14. In the census for 1880 your Andrew would have been too young to go by his own surname, just listed with his parents, so there might be another Backström or Bäckström who slipped away just before the census 1890. He may also have acquired the name Baxtre for some entirely different reason, of course.