Check and adjust your hand position on the shifter.
My advice is to keep your thumb off the shifter. Missed shifts often result from a driver's five-finger death grip on the shifter, which introduces unintended lateral movement that misses shift gates widely.
Pull the shifter with cupped fingers, no thumb.
Push the shifter with the heel of the hand, no fingers.
To make the First-to-Second shift, pull the shifter straight back; remember cupped fingers and no thumb.
To make the Second-to-Third shift, push the shifter toward the radio; remember heel of the hand and no thumb. This will allow the shifter's strong centering device to find the Third gear shift gate.
To make the Third-to-Fourth shift, pull the shifter straight back; remember cupped fingers and no thumb, same as the First-to-Second.
Conduct shifting drills, using the Step 1 hand positions.
The key to strong shifts under heavy acceleration without missing them is practice.
During fast shifting, the left foot goes on the clutch with the heel in the air, not on the floor. The left foot is always either suspended over the clutch preparing to shift or on the clutch executing a shift. Again, the left heel never touches the floor.
For each shift, there are five movements: clutch-in, and throttle-lift; gear-change; clutch-out, and throttle-down. It takes practice to get the moving parts of each shift synchronized, integrated, and executed in minimal time.
Now do the full shifts with complete movements: First-to-Second, Second-to-Third, Third-to-Fourth...pause. That constitutes one repetition. I suggest five repetitions per set and two sets per session.
I do at least 20 sets of this drill per week, usually two sets at each end of my daily commute, and two sets in the staging lanes at the dragstrip before each pass. This routine embeds muscle memory and makes each shift a preparatory cue for the next. Consistent practice will put an end to missed shifts for most drivers, and make each shift much faster and nearly automatic. That in turn will free the mind to focus on shift points.
Tips for shedding a few more tenths
Once you are comfortable staging, launching, and shifting the car, the following small adjustments will help improve your e.t. and trap speed.
Increase the front tire pressure to 40 psi. This will reduce rolling resistance. Tires without pressure sensors can be set to 45 psi.
Manage the engine coolant temperature to ensure it is 195 degrees or less when staged. This generally requires cooling the car between passes and minimizing time spent at idle. The engine management computer progressively retards timing as the coolant temperature rises above about 195, reducing effective engine power.
Heat the stock rear tires by doing a burnout. This will improve traction on the launch and shifts.
Intensify your shifting drills to further reduce shift times. This includes doing more sets in the staging lanes between passes.
Focus strongly on attaining correct shift points. This is easier to accomplish once the shifts themselves are essentially automatic.
Make a logbook and faithfully record your performance. On arrival back in the pits after each pass, write down your impressions while they are fresh. Study the entries later to identify and correct patterns of technique inconsistency and wastage. Not everyone has the discipline to keep a logbook, but if you do, I guarantee it will help make you a faster, more consistent driver.
Taking care of your clutch
C5 and C6 Corvettes driven aggressively often fall prey to clutch pedal issues during or following high-rpm shifts. The general symptoms include a clutch pedal that becomes lazy, hard, soft, hangs midway up, or sticks to the floor. These behaviors are commonly called clutch pedal woes. I struggled with this problem on my '01 Z06. Chevrolet's solution for my car involved swapping out all the clutch and hydraulic components. Despite that, my pedal woes returned within weeks. It was clear to me a better approach was needed.
I found through experimentation that keeping the clutch fluid fresh and clean solves the problem and precludes its recurrence. And I became an advocate of what is now sometimes termed the "Ranger clutch fluid protocol."