I've flown in Nepal this April. I didn't get up over 6000m this time but it sure had no problem at just under 4000m. No difference in power or control at all. And that was just a P2V+ - the P3 has more power and should be even better. DJI says 6000m but I bet it flies even higher. One problem with the P2V+ was getting satellite coverage. Many of the valleys are so hugely deep there that you get almost nothing. Getting 6 was lucky in many places. Again the P3 should be way better. I so wish I had mine for that trip, but am going back next year - with a P4 or whatever is available then.
Carry it on in your backpack. Make sure you bring your batteries with you, not in your checked luggage. Supposedly you should travel with them discharged (or at least 50%) but no one ever checked other than a Canadian customs guy one time who asked if I had enough charge to give a demo flying around in the inspection area (I declined). I flew on a couple of flights within Nepal on Yeti Airlines and Tara Air without a problem, but the inspectors didn't look entirely happy really. One plane was so small there was no way the pack would fit in the carry one - super lucky the seat next to me was vacant.
They are sticky in Nepal about flying in urban areas (Kathmandu/Pokhara) - but I did it anyway and had no problem. My friend who lives there and flies his P2V+ has been lectured by the police a couple of times in Kathmandu but no fines. I flew just before the earthquake (we left early in the morning the day it happened) and I heard they are more sticky now since so many people were flying around after the quakes. Have a great time and post some footage here! I am still working on mine.
I flew there through Dubai - also no problem with drones. Flying there was fun too!
Here's one quick shot of Kathmandu: