Much simpler - but too avant garde?
There was a lot of flashy displaying of high-power lasers a decade or more ago, blowing up objects like a missile, etc. Including ideas of putting such high-powered lasers into fighter jets for that ultimate space cadet feeling, bullseyeing womp rats from ... how many metres, again?
I'd say a much easier way to move a space junk pile is to send a asteroid nudger, with one of those high-powered lasers and enough propellant that it can match velocity and orbit, stay in orbit and change orbit for as long as necessary. Then from a distance of a few thousand kilometres, blast the space junk pile with ablative blasts in the direction of orbit. A steady set of such laser blasts won't tear the asteroid to pieces, but it will shift the material, and the ablative blasts will change the orbit somewhat.
The great advantage of doing it bit by bit, piece by piece, is that you don't have to get it right the first time. You can do it over a few months, and apply corrections if you find you've hit a snag of sorts.
My 0.02c worth, and don't spend it all at once.
Biting the hand that feeds IT
