I think you are seriously underestimating the complexity of this endeavour. I suspect it would be easier to clean the North Pacific Gyre with a tea strainer.
Try catching a leaf falling of a tree in autumn some time. Thousands of leaves falling, everywhere, all the time. And yet, you are never in the right place at the right time.
One could probably sail to the middle of the Gyre, toss a bucket over the side and haul it back up, and find nothing but... water. You might see lots of trash float by, lots and lots and lots, but never grab a single piece.
And it is the same with space. Sure, we are led to believe that near space is full of all sorts of shrapnel ready to drill holes through delicate equipment like space shuttles or, heaven forfend, people. Go up there for a week, and you'll wind up shredded like character in a Tex Avery cartoon.
I think people forget how utterly vast space is, even low earth orbit. You are simply not going to rendez-vous with so much as a 2 inch bolt.
I also think you underestimate the mass the reflector would need to be of any use. Unless it was solid metal several centimetres thick, anything colliding with it would just drill right through. If you have sufficient mass to make it useful, you won't have the energy available to move it around. Make it light enough to move around, and you won't be able to do anything, it will just be shredded like a hand going through a rice-paper screen.
God, I sound like a hippy but still, I say we should avail ourselves to cleaning up the oceans. The heavens can wait.
• another intruder with the mooring in the heart of the Perl