Your skill will accomplish
what the force of many cannot
I don't have energy to respond to this in full. However I am sad to tell you that you're mistaken on many counts. For instance contrary to your claim that I've implied that atmospheric drag begins at a low level, I've said that atmospheric drag will bring junk back to Earth in a time frame typically measured in centuries. (I just double-checked it and found I was wrong. While pieces from that may go for centuries, a lot of it will get fixed much faster.) For another example you got the relationship between size and orbital decay exactly backwards - larger pieces of junk experience more drag but have far more inertia and inertia wins. The same scaling principles that makes small things more affected by air down here operate in space. Another simple mistake is your claim that small particles are in streams. Consider the Chinese space satellite collision - that generated an estimated million pieces 1 mm or bigger and I guarantee it is not in a stream! Also even if you start out with a stream of small particles, miniscule velocity differences will, over the course of years, result in them being many km apart. And even if the initial speed was the same, differing effects of atmospheric drag would move particles apart.
Also there are major difficulties that you are minimizing. It is true that I assumed that you need to rendezvous with the junk to deal with it. It is true that you can more easily find collision courses with it. But read Re^7: "Practices and Principles" to death for how difficult it is to work with collisions at that speed, and recall that any shrapnel is new junk. I think my assumption that you want to match speeds holds!
This may be a good point to point out that a satellite in a Molniya orbit as you suggest using is going to be very far from still relative to any piece of debris it encounters that is not itself in a Molniya orbit. That is because while the satellite is fairly still relative to the Earth's surface, the piece of debris is nowhere near still relative to the Earth's surface, so there is a large relative velocity. In fact this is a general principle. If you encounter a piece of debris and at the point of encounter you do not have a large relative velocity, then you and the debris must be on very similar orbits! And conversely if you're on different orbits, any encounter will be at high velocity. The reason is simple, it is because from your position and velocity you can calculate every aspect of your orbit. So if your position is the same and your velocities are close if and only if you're on very similar orbits.
As for reusing existing spacecraft, review the link above about what collisions look like in orbit. Consider well that shrapnel is new junk. And then I think you'll agree with me that this is an approach that is more likely to create problems than solve them.
This is hardly an exhaustive list of issues I can come up with. (For example I didn't want to get into economic issues.) But it is enough to show how hard it is to solve the problem of space junk.