Answer to the dct, after having a'12 and '14 Ford Focus with dct the low speed shutter is pretty normal. In my case with the '12 the main input seal keep leaking and required 5 warranty clutch pack changes. They finally got it right the last time. You can check with the dealer to see if there is a software update that will allow the dct to engage a bit more aggressively. Ford was able to do it for both my Focus which pretty much eliminated the shutter.
As for the delay, if you really feel it is the clutches then definitely get it back to the dealer. In my case (I have the 2.0 Auto) the delay in accelerating is waiting for the engine to "come on the cam", waiting for it to reach 3000-3500 rpm and I am also hindered by the **** throttle cut off because I am a left foot braker when I drive an automatic. The Focus had it but allowed a little leeway where as the GT instantly cuts the power, so the car goes flat and even though I've had the car for a year it still catches me out especially on the highway where I want to get the rpms up to "squirt" into the other lane.
Also in my case I was unable to find a GT Sport anywhere within 700 miles that had the package and color I wanted so I went with the base with style and tech and will say I wise I had more power but I am pleased with the car.