Given that you have unlimited funds, here’s my offer: I’ll work on the question and have an answer for you within two months.
I’ll commence to working on the problem upon receipt of your retainer cheque in the amount of £566 million.*
*(and its subsequent clearance at my financial institution. I apologize for the apparent expectation that you might b e inclined to renege on the deal, but look who the titular leader of my nation is!)
Besides the destabilization problem, here’s also the issue of what exactly constitutes the base of Mt Everest. The base of the mountain blends in with those of the surrounding mountains. This of course, also goes with the question of how low the mountain is to be removed.
As for the drone helicopter using the NASA Mars tech, it might be able to make it to the top, but could it haul an appreciable payload up there? Remember the Earth has three times as much gravity as Mars, and that’ll reduce the payload. Also, how often are the weather conditions up there such that the drone can fly? There’s more air at the summit than on Mars, but that means the winds are stronger and conditions are likely not suitable most of the time.
I would say that the common usage when someone says “level” something, it’s to bring it down to the level of the surrounding area.
Looking at a topo map, Everest could be considered to be more triangular shape but it’s not just a mountain by itself. It’s part of a chain of them, so, that actually adds to the volume to be removed. But, going easy on ourselves of 3km for H and 5km for the base, we have 2,500,000,000 cubic meters of rock to remove. One of those Baggers can move 240k cubic meters of material a day, which is 28 years.
Given unlimited money, seems to me we could attack the problem in multiple ways.
OP specifies a neat level plain, but not how big the plain must be–that is, we don’t have to make a level plain with the same notional footprint as Everest.
Neither does OP specify the height above sea level. I don’t know enough about Everest to figure this out, but let’s pick a point above which, if the mountain were removed, you wouldn’t bother to go. This’d still be pretty high but below Base Camp.
Next, we have access to B-52s and smart bombs. Money is no object so these are all rebased near Everest and kept flying and filled to bursting so we can pound down the top of the mountain.
Simultaneously, dozens (hundreds?) (WE CAN AFFORD EVERY ONE IN THE WORLD!) of tunnel boring machines are working the base of the mountain. They tunnel in, charges are set off to bring down a massive landslide, and thousands of trucks haul away the rubble. The tunneling machines may be lost because it’s too slow to back them out but who cares, here comes the next wave we bought.
As appropriate our B-52s and later C-130s with MOABs keep pummeling the top. At some point the new summit is low enough to land helicopters, meaning the ability to land heavy equipment to keep blowing up the top part of Everest. At this point it gets more efficient because if done right you blast the rubble down the side away from the tunnel borers.
Eventually you probably switch over to all tunnel borers/blasting, and then to a fleet of Baggers.
Given all the money in the world, I’ll say 30 years. Completed just in time for humans to go extinct because so many resources were poured into this project instead of combating climate change.
I’d think the driver of the high altitude mining vehicle would be in a pressurised vehicle cab breathing pumped-in air compressed to something like 1 ATM. That much is achievable with current technology. Getting the vehicle up the side of them mountain is going to be another matter. Probably requiring more than minimal modification.
I fairly regularly spend four or five hours at a time at higher elevations than Everest, with minimal effects. There are even people who do it nearly every day, as a job (some of them on this board). I’m pretty sure we could apply the same technology to trucks and bulldozers, if money was no object. People would still need to get out of the cab once in a while, but if you’ve got a vehicle to carry your oxygen, you can bring enough so that your mask goes at a high enough rate that an hour here or there won’t create health issues, I would think.
I don’t understand all this talk about “safety” and “optimum placement of munitions”, etc. Just make an announcement to the population that there will be incessant B-52 bombing of the mountain until it is reduced to rubble. They can drop MOABs, which cause the most damage there is short of nuclear weapons.