Good corrections to my assertion about symmetrical airfoils for the horizontal stab.
Angle of incidence would be lower for same downforce, so might reduce trim drag somewhat.
My experience was with light planes and fighters. Even some lights had all-moving tails like my fighters.
I think the main lesson for the questionor is it's all about the CoG versus the CoP, and what happens to a "trimmed" plane if you have an "upset". Moment arm of the tail due to distance has an impact, but not as much as the CoG versus CoP, IMHO.
Good discussion.