Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.
Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.
If you're talking about intuitions, you have no firsthand intuitions about lifting effort decreasing with distance to the Earth. We can intuit about constant gravity, and the math of constant gravity works fine for this description.
And while the real situation at scale is more complicated, the math is going to come out to the same answer, albeit with extra terms muddying everything up.
If someone says that something true can be illustrated intuitively with a thought experiment, "sure, but what if we take that to a scale where our intuitions fail" is a sort of odd place to take the discussion unless you're genuinely curious how the math is going to shake out.
On earth, it just about is... you haven't scaled up enough. Low earth orbit doesn't have much less gravity, it's just that there's no air resistance so you can move fast enough sideways so that you don't run into the earth. Hence orbit and not just floating.
But more to the point the kinetic energy here is being turned into gravitational potential energy. If you move to a place with a weaker gradient in gravitational potential of course the same amount of kinetic energy moves you farther up.
What intuitive understanding do you have of moving furniture up 10,000 floors? None.