Earlier today I was out riding, and I decided to see how my '89 VN750 ran at high (6000-ish) RPM's.
I noticed that as I approached this, the bike seemed to falter a bit and lose power. Problem went away as I switched to next gear.
Is this normal? If not, what would be the issue, most likely?
No, this is not normal, your bike should pull steady all the way to redline.
How did you approach 6k rpm - WFO or just sneaking up on it slowly?
Done any mods to your bike from stock?
As to the pilot screw...let me suggest that one turn of the pilot screw has about enough effect on your system at 6k rpm as removing 3 lbs of weight from your bike makes it faster. Technically, yes it's true, but it's so inconsequential that you'd never notice it - and neither will your engine at that speed.
The pilot screw is part of the pilot circuit - it has little to no effect on your engine after about 1/8th throttle.
If at a steady state cruise, your bike is hiccuping or missing a little, it could probably use the needles being raised by a washer or two.
If at WFO it misses noticably in the upper rpms, you likely need a bigger main jet.
If you haven't modified your bike at all and it's doing this, I'd check the condition of your air filters to make sure they aren't deteriorating and letting little bits of foam get sucked into your carbs and plugging up the air jet passages at the mouth of the carb inlet...and then I'd pull the ducts coming from your airbox and inspect those three little passages at the bottom of the carb mouth to visually verify that they're clean & clear, and maybe shoot some carb cleaner down each one for good measure.
Hope this gives you a little more direction as well as explanation.