The fast twitch, slow twitch characteristic is just theoretical. Basically, someone who is faster twitch will be more explosive, and have much less endurance than someone that is more middle of the road... People who are slow twitch dominant tend to be able to squeeze out several slow reps of an exercise, where as fast twitch dominant individuals, may bang out 4 reps and have the 5th come crashing down on his head. That is because these muscles are not oxidative, and type 2A have basically no endurance characteristics at all. But to answer your question, there is someone change of fiber type. With a repeated stress muscle fibers will change, fully I believe from one type to another, now I know type 2A can switch to type 2b but Im not sure about type 1 switching to type 2 and vice versa.. I have an article I have to find for this.. But I dont think given your goal you are training incorrectly.
However, there may be occasions where you want to up your volume and rep schemes to see some increase in cross-sectional area (8 reps or so), then you should increase your ceiling for strength with that larger muscle area. You also may do well with emphasizing the eccentric portion of the movement, occasionally, and at a set time in your program.