OP, does your Dawes tourer have cantilever brakes? It isn't obvious how they should be set up to get maximum braking, and new bikes straight from the factory have been known to be badly set up. If the brakes are properly set up, you will be able to lift the back wheel braking from the hoods, and you can't use any more braking power than that.
You shouldn't need to go down on the drops to get effective brakes.....and if you do go down on the drops your weight is more forward and the back wheel lifts too easily, and you actually lose effective braking.
It is important that braking from the hoods and the drops are done differently.....from the drops its a squeeze with your fingers, from the hoods its done by flexing your wrists to pivot your hands around your thumbs which rest on the brake hoods.
I think any
reply about bike riding position should begin with the caveat "....It all depends how you set your bike up in the first place...."
As you will see from my bit about bike fitting, I set my bikes up so that I have very little weight on my hands when my hands are on the hoods and I am freewheeling. People from a racing background (and people younger than me) often set their bikes up so that they have much more weight on their hands freewheeling, but strenuous pedalling takes the weight off their hands. (Strenuous pedalling is, alas, just a memory for me....
I personally don't like crosstop levers at all, they make my riding position much too short reach, and I have much more control of the bike with my hands on the hoods. However, for somebody who sets their bike up with a much longer reach than I do, their crosstop levers may be at about the same reach as my hoods.
Just for fun, heres a publicity photo we took https://www.flickr.com/photos/52358536@N06/32996195254/sizes/l/
I'm on 28mm slicks, and the green stuff is wet and slippy......So I'm in the position that gives me most control.....hands on the hoods, weight well back.