This is a revived older thread, but I thought I'd add my thoughts for what they're worth. I'll address your points D-VO for the sake of convenience.
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Originally Posted by D-VO
I normally skip gears as [I] drive and typically shift 1, 3, 6. A couple of days ago I revved 3rd gear out to about 5k rpm, shifted into 6th and had a really bad grind.
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Your synchromesh mechanism is worn, worn more than it should be at this time. It is worn BECAUSE you have skip shifted repeatedly, which puts UNDUE WEAR on the synchro ring as it attempts to synchronize the speeds of the two shafts and their spinning gears so that they may mesh smoothly.
When one shifts from 3rd @ 5000 rpm straight into 6th (skip shifting TWO gears), the disparity in shaft speeds is far GREATER than it is when shifting 3-4-5-6, sequentially. Matching these "wildly" disparate speeds is what is causing extraordinary wear on the poor, long-suffering 6th gear synchro ring … and it's wearing out and dying an early death in consequence.
Also, shift slowly enough to allow the synchro ring to match the shaft speeds so the gears mesh when possible. Forcing a shift, speed shifting, also exerts undue wear on the machinery. It's quicker, yes, but it comes at a cost. Some gearboxes are sturdier than others.
If you have not had your gearbox repaired, you might want to try this "trick":
Take it up to 5000 in 3rd (as you described). On standard tires that is 56.3 mph.
Now, your 6th gear will be spinning at 2489 rpm at 56.3 mph.
We want to match those two speeds.
De-clutch. Shift to NEUTRAL.
ENGAGE clutch in NEUTRAL.
Bring rpms to ~2489 rpm (less as road speed drops). Use the throttle as needed.
Now shift into 6th gear.
There should be NO GRIND.
In fact, if you've matched the revs exactly, the gear lever should drop effortlessly into 6th WITHOUT even using the clutch.

But, one should always use the clutch anyway, because it's virtually impossible to match the gears EXACTLY and with the engine driving the input shaft, we're back to suffering excess wear on the synchros if we do not use the clutch.
You've just performed a double-clutch UP-shift.
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I guess the problem now is since I'd like to race, the 6th gear grind will soon turn into a transmission rebuild.
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Perhaps, but that depends on the track. You'll see 128 mph at 7400 in 5th gear. That may suffice for most tracks. If not, learn to double-clutch and match revs on the upshifts. Here are the speeds at redline:
5th @ 7400 rpm = 128.3 mph
6th @ 5676 rpm = 128.3 mph
In other words, engage 6th gear when the revs are at 5676 rpm @ 128.3 mph (in neutral, clutch engaged) … and the lever should slide right in with no grinding whatsoever.
YouTube has many useful videos to help one understand how a gearbox works. Watch, study, and think about it and you'll come to understand why this "trick" is working. Accompanying this will come the understanding of WHY one should not skip shift without using the double-clutching technique to match those shaft speeds, and thus minimizing the wear on the synchro rings. All of that is far more than I can explain in words, here.
Oh, and you may wish to find the thread on s2ki.com about a Honda engineer discussing why it's really bad to skip shift on their gearbox. That's what first opened my eyes, and you may find it equally useful.
I hope this has been helpful. (And I hope I got this right, but if not, somebody please help us!)