I don't see why you couldn't generate stably expressing Expi293 cells though I have no direct experience with this. We do work frequently with 293T cells. For what you are describing, I think the most efficient method would be to generate your library in a lentiviral expression vector with a selectable marker. You would then package the lentiviral library in 293T cells, infect your Expi293 cells, select for stable transductants, and then screen for mAb binding by FACS. But would the soluble E protein constructs simply be secreted into the supernatant? I would think that you would need them to be expressed on the cell surface.
puromycin is a good marker - it kills nontransduced cells quite quickly. We have also used blasticidin and hygromycin with good results. One word of caution; 293T cells are resistant to G418 (neomycin resistance). I don't know whether this applies to Expi293 cells or not.