Your guess that the blockage moved further downstream is certainly correct. In addition to what RP suggested, you could also try to snake through a roof vent, or locate a cleanout just upstream of the clog and snake through that. You need to be very careful working on a roof. Sometimes (with smaller twisty drains that are difficult to snake) I like to try using one of those rubber drain weenies that you attach to the end of a water hose and push a few inches into the pipe. They force water under pressure that can sometimes blow out a clog. You need to be careful to block other drains and overflows. They come in sizes that will fit 1 1/2″ to 4″ pipe.
NtP