What if, you go to the top of the mountain, can't be too hard if its only 2000' and take off from there, would the A/C set that 2000' limit and you could fly higher from there?
It's not a viable solution.
Yes, theoretically it can work, but you have to find a landing point absolutely safe, flat and always in sight, so a lot far away, not near the mountain.
The high risk of losing the signal with your drone immediately after the landing because the antennas on the legs are shielded by elements present at that point, stones, plants, grass, even small rocks, of which it can not be established with certainty even after repeated previous flights and hoverings, their precise size and height.
Generally the mountains do not have favorable places to do this, they should be made like the pyramids of Egypt.
It's also the high risk that the drone will laterally banks, upsetting at landing if the surface is slightly inclined and has detritus rocks and there is wind.
Potentially solvable if you add large extensions to landing gears, longer rigid legs and extended to the outside, or large lightweight elements made of expanded polystyrene.
However still something that can easly take to a point of not return, maybe good for a very very limited kind of locations.