I'm not sure what your math is because you're not showing us any. But it sure doesn't agree with mine.
Math is done with numbers, so let me give you actual numbers. You can double-check these against https://en.wikipedia.org/wiki/Orbital_speed#Tangential_veloc....
Standing on the surface of the Earth your potential energy relative to infinity is −62.6 MJ/kg. If you were standing still 160 km up, you've added roughly 1.6 MJ/kg. (You climbed 160,000 meters against a force of 9.8 Newtons per meter.)
To then go into orbit you have to add a sideways velocity of about 7800 m/s. Apply the famous kinetic energy = 0.5mv^2 and going into orbit requires 30.4 MJ/kg of energy. That's 19x more energy than is required to get to altitude!
But it gets worse! If you're going to go into orbit, you need to think about getting down. Going up we go straight up out of the air and then add sideways velocity. Going down we let the atmosphere do most of the work of slowing us down. But in order to survive that you need a much more rugged device with a heavy heat shield. You're now both doing more work per mass lifted AND you're lifting more mass!
But we're not done with the bad news. A fundamental fact about rockets is that you have to lift the fuel you use later in the launch. That means that as you're increasing the final velocity you're getting an ever-decreasing ratio of energy expended to useful kinetic energy for your payload.
Put it all together and actual rocket scientists have told me that it is about 100x easier to get to orbital altitude than it is to actually get into orbit.
That said, LEO is the half-way point. Getting into LEO takes about as much energy as it does to launch from LEO entirely out of Earth's orbit.