No, the two triggers from Spell Queller are placed on the stack (your opponent chooses the order) as soon as Eldrazi Displacer's ability has finished resolving, at that point a target must be chosen for the first ability. So even if your opponent orders the two abilities so that the "may cast" ability resolves first, the Transgress the Mind will not be exiled again, since it couldn't be targeted at the time the "exile target spell" ability was put on the stack.
If i use my eldrazi displacer to blink spell queller and i choose to cast the exiled transgress the mind, when spell queller returned, can it exile my transgress the mind again?