The nose-up couple at T/O thrust is significant due to the low-slung engines, and will unweight the nosewheel to some degree, reducing steering effectiveness. If you look at FCOM 3.03.08 P3 GROUND RUNUP DANGER AREAS you will see that the exhaust gases pass the outer half of the tailplane and elevator at over 65mph (CFM) and 68mph(IAE). This is where the upforce on the tail comes from at low speed.
FD
You seem to have gone from "it really is FULL elev down" to "I am pretty certain that half stick gives full elevator down with IAS=0" in one post!
From FCOM 1 : "Ground mode is a direct relationship between sidestick deflection and elevator deflection, without auto trim." Why would half sidestick deflection give full elevator travel? Please explain because if what you say is true
1. I have been labouring under a misapprehension during all these years of watching flight control checks
2. The different procedure in a tail or crosswind is pointless.