The OE 1LE shifter being a short throw relative to what? An IROC?
For the average Joe, I feel like if you're missing your proper gear gate, your muscle memory hasn't sync'd with your reflex speed, or how fast your arm/hand is capable of moving. Much like a gun-slinger, anybody can whip their pistol out fast, but it takes practice (and talent) to pull it out where it needs to be. Same for shifting fast. Assuming no mechanical constraints, throwing the shifter to the next gear is just knowing where the gate is. If you're going from 2nd to 5th, you're obviously not in the right place.
Also, the OE shifter is relatively light, so it does take some effort particularly when shifting quickly. A weighted shifter knob may help some. Most importantly, be mindful and deliberate when shifting fast. The 6 speeds spread the power curve further compared to an auto, so there is plenty of time between gears to mentally prepare yourself for the next gear. If you get flustered or lost while in "gun-slinger mode" you may wind up shooting yourself in the foot, or money shifting the car. Going from 2nd to 5th at WOT isn't a pleasant experience for your drivetrain any more than 3rd to 2nd.
As to whether an Aftermarket Short-Throw would be the cure, it's an unknown. I would say if your muscle memory is more in tune to a shorter throw, perhaps it would help as it would be more familiar. But if not, it could make things worse since your muscles would have to relearn your shift throws from scratch. I've watched some really talented manual drivers shift the OE shifter mind-blowingly fast, so it's completely do-able without an aftermarket replacement. Ultimately, if you're building the car for competitive use it's probably worth doing and relearning. Competitively you'll want every advantage you can get, particularly when squaring up against a modern Auto.