When I attempt to memorize the song, I look off to a vacant corner of the room, eyes open, putting the lyric page or book down just out of sight.

And I'm with you about singers closing their eyes during performance. I try not to do that. With old songs that I have been singing it is easier to do; with brand new material, it is more difficult. But rather than close my eyes, I tend to look somewhere off in the distance, without making direct eye contact with individual members of the audience. This is probably just as bad as closing my eyes. However, if I do this, I can concentrate a little better. The answer of course is more practice.
Jim