Not a wildly popular answer but I hope you'll consider it -
Many top players never CONSCIOUSLY chose to work on their preshot routine. No, I have no proof of that. But I think preshot routine is misunderstood. Preshot routine doesn't cause good shooting. Good shooting causes preshot routine.
Basically you hit a million balls, and take FULL CARE on each one, skipping and rushing nothing in terms of planning and execution. If you treat all the steps as important (even on the easy shots), you'll end up doing effectively the same thing on every shot. There's your routine.
I know, preshot routine is just one of your steps. But let's just call what you're talking about the entire shot routine. Same advice applies.
When someone talks about making something more rhythmic or less scripted or smoother, what they really mean is "faster". Oh wait, you actually typed it outright =) Let me ask you, why is faster better? When guys are playing in the us open... how many of them seem to be shooting fast? You see shane, ralf, mika, or johnny winning majors 'faster'? Who got it in your head that you need to speed up? Maybe your opponent?
At this point someone will point out that it's not the speed, that it's the rhythm, virtually every shot seems to go the same way. I won't argue with that, you can detect a clear rhythm in guys like earl and efren going 1-2-shoot, 1-2-shoot.
What I'm gonna say is that focusing on it will not help you as much as following all the important steps and allowing it to happen naturally.
This is especially true about "Preshot routine" - some guys focus excessively on foot placement, how your bridge hand gets onto the felt, how many practice strokes you take... overthinking these things can put the Mongolian Death Jinx on your shooting. They will all come naturally from hitting a million balls. Use common sense and get into your stance comfortably and change it if it feels even a little wrong. Don't sweat how many practice strokes you're taking and NEVER shoot a ball before you're ready to fire. If that takes a while, so be it... but it shouldn't take a while unless you're subconsciously stressed by the shot in some way. If you find yourself sawing wood uselessly, it is a sign of being unsure about the shot. Probably you need to go back to the planning stage and figure out if something's bothering you and if you wanna change the gameplan. If not, commit to it and shoot it when you're done aiming.
Evaluation's gonna happen automatically and you have all the time in the world to do it from the chair if you missed the shot or blew shape badly.
Don't hesitate to go to one of the instructors. I may disagree slightly with them on this subject but I have no doubt they can and will improve your game.
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