The same incident happened to a B737-800 2 weeks ago in Germany. The effect of applying full nose down elevator will do abosultely nothing to help this type of incident as the movement of elevator does not change the CG.
If the loadsheet looks right then the Commander will sign it. It is impossible for the Commander to check every piece of luggage (position and weight), check the passengers are sitting where their boarding card says they should be, etc. This kind of problem is caused by inefficient training by the ground handling company.
When the tail stuck on the B737-800 the aircraft was doing about 5kts groundspeed and it was the fuselage that struck the ground, not the tailskid.
Something to keep in mind about the B737