Konigsberg (today called Kaliningrad) has a seaport that does not ice over in winter. So, the story of Dovid bringing groceries from Kovno to Konigsberg makes sense, if they were goods being shipped out.
Port of Kaliningrad
You may want to research what records exist for Kaliningrad, and see if you can find anything on Max or Dovid.
Also, did Dovid stay there, or did he emigrate? For instance, if he came to the U.S. you can search for naturalization, passenger manifest, and other records which may lead you to an answer.