Unless one has a very small shooting window which is the sign of a poor target setter, "fast" targets are mostly due to picking a point too close to the trap to pick up the bird. Look a little further out and the bird will "slow" tremendously. Adjust your insertion point correspondingly and "fast" birds will be easier to hit.
A poor target setter is also to blame if black targets are thrown against a dark background. If black are set against an open sky, then it is a poor target read by the shooter which causes most misses.
I tend to shoot Imp Mod in my barrel(s) no matter distance. The center of the pattern is the same size no matter the choke and I never wonder if I am under choked for any sporting clays presentation. I use Mod/Full or Full on occasion as my fixed choke guns are choked such. This year's league will be shot with either a 16 ga SxS choked Mod/Full.
Sporting clays and 5 Stand are fun but my passions are old style FITASC, Compac, and Helice/ZZ bird. FITASC is the French version and the targets typically are further out. Mod is the most open I'd use with IM/Full being used by far the most. The shooting order and course of fire is different too making the game more interesting. Compac is kind of a mix of 5 stand and FITASC though I kind of get confused as a local coure's version is a bit different still. Helice is similar to live pigeon shooting and is a real test of skill and some luck.
