The idea of deriving some energy and momentum from the captured debris is interesting. But I'm pretty sure it will not stand up to critical analysis. The relative speeds of orbits crossing through the same area in space at different inclinations or eccentricities are faster than a bullet. Even if the net survives this many types of debris captured certainly won't - they will shatter and generate lots of smaller pieces of debris. If you somehow manage to choose only encounters with speeds low enough to survive the impact it will be too slow to derive any useful energy or momentum from. This idea might be sound in principle (though I wouldn't bet on it) but wrong by several orders of magnitude in practice.
And no, Cringely, you can't simply "trade altitude for speed" (potential energy for kinetic energy) in space to change to a different orbit. While it does not break the law of conservation of energy it definitely violates conservation of momentum. You could change momentum without spending energy via gravity assist with a third body (nothing available with enough mass in the vicinity but the moon) or using a tether. Otherwise you need to spend energy and reaction mass to change to a different orbit even if it has the same orbital energy. Space tethers are sometimes proposed for collecting space junk by people who actually understand a bit of orbital mechanics. Tethers are a very complex and mostly untested space technology we haven't mastered yet.
Capturing all 18000+ objects in a single net?!?!? What are you smoking? Have you any idea how much mass you are talking about? Moving all this mass to all the target orbits is an unimaginable waste of delta V. Even if you could somehow derive some momentum from the captured debris the 100th piece captured will barely change the vector of this huge collected mass.
Yes, as you say, this is a crazy idea. But it's not crazy in the "crazy enough that it might just work" kind of way. It's just plain crazy, dumb and ignorant.
Sorry, Cringely. You have just lost whatever remains of professional respect I still had for you.