

KSP player here. So, you know, ignore me.
But let’s consider how you’d rendezvous two objects. You’d want your asteroid to have an orbit around the Sun that is very nearly the same orbit as Earth’s. A perigee that just kisses the Earth’s orbital ellipse and an apogee that’s slightly further from the sun. You’d want the asteroid to approach its perigee at the same time as Earth approaches that same point in space. Then they’d have very close to 0 relative velocity, with the asteroid moving slightly faster around the Sun than the Earth. So you just bleed off some of the asteroid’s velocity through whatever magical explanation you want… such that your asteroid has 0 relative velocity with Earth, giving it the exact same orbit as Earth. I.e. from Earth’s perspective it’s just floating there motionless in space.
Problem is that this only works for a rendezvous between two very light objects with very small gravitational effects between them. The Earth is massive enough that the effects from Earth’s gravitation would overtake the Sun’s as the asteroid approaches Earth. Then, yeah, the asteroid becomes a falling rock with a lot of energy so I don’t think any of this works.
I think the problem that you’re going to imagine a good analogy for this is that orbital dynamics works in sort of (but not really) an unintuitive way.
An object in an elliptical orbit around earth is moving slowest at its furthest point from the earth. Like a thrown ball that slows when it reaches the top of its trajectory. That object is moving fastest at the point that it’s closest to earth.
So you have this dynamic where if you decelerate it changes your orbit such that you’re increasing the speed you’ll be moving on opposite point of your orbit. E.g. if you decelerate at your slowest (furthest) point, it brings your closest approach point closer to earth and you’ll be moving even faster when you get there.
You can decelerate at your closest approach point but eventually it brings the opposite end of your orbit closer to earth than you are, and then you’ll fall and of course speed up again. There’s no real way around this. You’re going to be moving fast when you approach earth unless you’re doing a lot of very active deceleration.