Watching 737-800s takeoff a lot, and having to rotate my non-737 at 2.5°/sec, I'll wager that 2-3°/sec is not used during most rotations. It is obvious that the rate drops off a lot as unstick occurs and is nowhere near 2-3°.
My bet is that your FDM slow-rotation witchhunt will result in tailstrikes.
The rotation rate is academic on 2 engines.