Mine are pretty similar. Although different frames with different Effective TT and BB heights changes things a bit.
I think I probably spend more time in the drops in a cx race than a road race. I run shallow drops so it is comfortable and not overly stretched. I prefer the stability when terrain is difficult. I don’t really think there is much aero advantage as speeds are often <15mph unless it is a fast dry course.
On my road bike I spend time in the bunch on the hoods, the odd corner and sprint in the drops but when I’m in the wind and riding tempo (in a break or chasing one) I prefer hands on the hoods with forearms on the bar which is my default TT position since I don’t use tri bars.
You need to use your bodyweight to hop. If you are pretty stretched out on the longer dropped stem then you won’t have much movement in your torso to start the motion.