I'm not sure if the answer is still relevant, but I own the XR650L big red pig and may say that it's rather safe to mess with the carb of this bike even if you don't have specific skills. It's very forgiving unless you do something really wild. I used to ride about 500 km on my with mixture being extremely lean and was lucky enough to have my engine undamaged.
Second is that I confirm that this bike feels relatively sick at these altitudes due to the mixture being too rich for a given air pressure. You'll need to lean it a bit. But first you have to confirm running rich. The simpliest way to do that is getting out your spark plug and inspecting its color. Please carefully clean the engine and the cylinder head before removing spark plug to avoid even dust entering the cylinder.
Spark plug should be dark brown, you can easily find pictures with proper color over the internet. I'd bet that yours is completely black. By the way, replacing spark plug with iridium one may help a bit with engine stuttering, but doesn't solve an issue completely.
Put the spark plug back in (using a tiny bit of motor oil on the spark plug threads (not the electrode, just threads) will help reducing risk of stripping cylinder head threads) and get to the carb.
I would say that first thing you need to do is grinding off the mixture screw tab as described in Dave's Carb mod here: http://www.4strokes.com/tech/honda/xr650lcarbmods/ Please also note that you don't need all these mods because they are enrichening mixture a bit, which is something you want to avoid, you need only the mixture screw tab grinding.
Anyway, mixture screw only adjusts the mixture when engine idling or running at low throttle while your stuttering should happen with the throttle wide open. Mixture at the throttle wide open depends much on the carb needle and the main jet so you will need to go for these parts.
When having your carb apart of motorcycle, please check if your needle is adjustable. If previous owner used any sort of jetting kit, it's very likely to be so. Stock needle doesn't have adjustments at all. You need to lower adjustable needle a bit to lean the mixture.
If the needle is stock then the ultimate solution is replacing your main jet with a smaller one. Stock is #152 and you may need #150. Find somewhere a #150 main jet that fits your carb and replace yours with that one. That should fix your stuttering issues completely.
Beware of any dust or sand entering carb or engine. Always operate in a clear room with proper tools. Get yourself an XR650L service manual - it's very handy. Think twice before acting. Buy yourself #150 main jet in advance - it's rather cheap. And always change one thing at once - e.g. never change both main jet and the needle altitude at the same time.
This all sounds complicated, but it takes about 3 hours to change main jet at this bike for an unexperienced mechanic.
After changing carb settings go for 30-50 kilometers ride, get back and reinspect the spark plug color even if the bike feels much better. If you make your mixture too lean (gray, almost white spark plug), it will feel good, but you could overheat and melt the piston.
Oh, and there is a simple solution to your problem, which is putting on an aftermarket exhaust with improved air flow. This will also lean mixture a bit.
