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^^All a short shifter essentially does is change the pivot point of the shift lever... which changes the leverage needed to get it in/out of gear. It doesn't help the car do anything- it helps the driver by giving him/her the perception of the gears being closer together; and therefore less 'sloppy'... resulting in a more 'connected' feeling to the drivetrain. The down side is that (like in your case), the added sense of precision will also amplify the driver's perception of any issues in the gearbox.
Yes, most drifters use a longer shift knob for comfort & ease of access during high speed, high-g driving... With a short shifter & long knob, the gears still feel closer together & more precise, but the extended knob gives better leverage than a standard-length shifter... and it's easier to get to without looking when alternating between the shift lever & handbrake.
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