Thanks for all the feedback, all!
I went out at the weekend with a friend into the Cotswalds from Bristol - he is not a fan of the main roads so we were on proper twisty, gravelly, steep lanes for most of the ride. I was consciously trying to look ahead and break the corners down, and also to "guide" the bike with my line of sight, which I think helped a little. I didn't experience any scary moments, and the corners felt more controlled - probably because I was cutting back on the speed a little earlier and a little more than usual.
Getting into the drops is something I'm going to save for the descents I know well (I've got a couple in mind to try out next weekend).
@zizou I am generally very comfy indeed in the drops on the flats and on open descents - the issue only comes on the sharp bends and a lack of confidence rather than comfort. I will have a look and see if I feel happier by shifting the hoods and brake levers a little so they are easier to grasp from the drops... At the moment the hoods are set perfectly for riding comfort, but reaching the brake levers from the drops requires a slight stretch at first, so I might have to compromise between the two here.
@palinurus - I must say I can't work out in my head quite how to make a right hand turn by pushing forward with the right hand, but I am intrigued and will have a play with this, thanks for the tip.
@Piemaster - yep, repetition is definitely the best way to get comfortable with any descent - and upgrading to disk brakes probably the next best way!