Your understanding of the structural twist is correct. And “yes,” the structural twist can certainly be independent of the aerodynamic twist in FAST (and in real life).
I’m assuming that the “MLx” and “MLy” you are plotting are taken directly from FAST’s bending moment outputs at the strain gages – that is, outputs Spn<J=1,2,…,9>MLxb<K=1,2,3> and Spn<J=1,2,…,9>MLyb<K=1,2,3> for the J’th strain gage and K’th blade. You should be aware that these bending moments are output in the local coordinate system determined by the structural twist that is oriented with the principal elastic axes and moves with the deflected blade. When the blade is undeflected, the principal elastic axes and the blade (pitch) coordinate system are related by:
xb = COS(StrcTwst)*Lxb + SIN(StrcTwst)*Lyb
yb = -SIN(StrcTwst)*Lxb + COS(StrcTwst)*Lyb
zb = Lzb
where (xb,yb,zb) is the blade (pitch) coordinate system, (Lxb,Lyb,Lzb) is the local coordinate system that is oriented with the principal elastic axes, and StrcTwst is the local structural twist angle. The bending moments can be transformed using the same transformation.
When the blade deflects, however, the blade (pitch) coordinate system is still relative to the undeflected blade, but the local coordinate system that is oriented with the principal elastic axes moves with the deflected blade, The transformation in this case is complicated by the slopes of the out-of-plane and in-plane blade deflections (which, in turn, are related to the contributions of each mode shape).
With this interpretation of MLx and MLy, I believe your results make sense. A large change in the structural twist will lead to a large change in MLx and MLy when the orientation of the applied loads is unchanged.
I hope that helps.