Drops are for going fast, not doing technical or rocky stuff.
The little brakes on the top are a bit pointless, too close together, not much power and on a narrow bit of the bar. Use the hoods, unless you’ve set the bike up far too long, or with the hoods rotated a long way forwards. Then your weight distribution will be all wrong, you won’t be able to reach them properly, and it’ll handle “skittishly” (terrifyingly).
There is a high wide position, the hoods.
Try something like woodchippers, they are shallower (so you don’t have to reach so much for the drops, and wider. And flared so you don’t smash your wrists on the tops when using the drops, and the drops are wider/higher, so you’ll get a more usable position in the drops.