My general strategy is similar. I tend to draft closers later than most (Saito, Fuentes, Valverde, etc...), usually about 3 closers is perfect. I then swoop up two top-notch mid-relievers (Neshek, Broxton, Otsuka) for ERA, WHIP and K bonuses to fill the P spots.
I like to have 1-2 great starters to bolster my staff, then I go for the late picks (Snell, Bush, Hill, etc...).
Hitting needs to be solid, but don't sacrifice pitching for hitting. I also keep a small hitting bench in favor of more SPs.
Remember there are an even number of hitting and pitching stat categories to win, and if you want to win your league, you need most of them.