Your comment on power cleans and powerlifting makes zero sense. I've seen the ridiculous number of form checks you've posted for deadlifts, so it might take you awhile to get the power clean down, but given your numbers you are probably a good candidate for them and should definitely learn the movement.
As far as the squats go -- I have a unique suggestion. Just do the ID on both days. You seem to respond well to training, it might work, for a little while at least. That's what I've always done. Besides -- who wants to squat 5x5 or 4x5, that's a bad time.