I'm not sure if this is happening in your case, but I used to have slow turning speed because I was turning too much with the wrists and less with the fingers. I'm getting better at breaking that habit, and have reworked a lot of my old comfortable "wristing" algs to be solely done by fingers. I would recommend to take a look at your F2L and see how often you use finger turns and how often you use wrist turns. Wrist turns are things like double layer d turns, cube rotations, doing U or U' turns with a thumb trigger and not using the other index finger, anything like that.
These wristing movements will slow you down. The other thing is like others have said I also recommend to try metronome practice. You might be surprised. It could be the case that your turning speed is actually a lot faster than you think, and because of that you are losing lookahead causing delays. I only get my fastest averages (sub-15) when I am concentrating very hard on not going too fast, allowing a balance between doing triggers but still being able to look ahead. If I trigger at full speed on every pair during F2L I get horrible times, becuase I have significant delays between pairs to find the next pair. Again I don't know if this is what is happening in your case, but it's just a thought to consider.
Hope this helps,
Chris
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