it could also have to do with the height of your handlebar (did they take spacers out during the fitting?) and the length/angle of the stem. my bike got more squirrely when the fitter removed a couple spacers.

Re looking behind you, maybe you can install barend mirrors or a helmet mirror.

switching to straight handlebars will cost $$ because of the brake levers&shifters you will have to install.

My opinion is that you probably have the same amount control in the drops as on horizontal bars, once you get the hang of it. You won't have really good control in the top bar position, so this should only be used in very safe conditions. You will have better control on the brake hoods (but less force on the brakes), but the best is in the drops (and more power on the brakes). So for descending go into the drops.

Turning tight corners, well, noone is saying you have to do it fast, and maybe taking a clinic on road skills would help. it helped me loads.
You'll learn how to corner, how to ride the ideal line of a bend, where your foot and your weight goes, and where to look when cornering.