Me personally would change a few things, but not all at the same time:
Firstly make the hooklink longer 8-10" to start with and see how you get on, because the lead may be getting plugged and the running part of the set up maybe not working as well as it should.
Secondly change from a Fox SSBP to a Fox SSC as the beak point may be glancing off the carps lip, as the lips may be soft due to the make up of the lake bottom.
Bait size is fine, and hair separation is fine, but you could play with this using extenda stops to make it just slightly longer.
If you still fail more than you achieve, then it may be worth using a piece of silicone on the hook to put the hair coming off the point bend instead of the shank bend, this makes the point heavy and when you try it in your hand the hook turns ready to catch the bottom lip, this can be further improved by adding a small blob of tungsten putty approx 2" from the hook..
Hope that helps, if not drop me a PM...