Well, I come bearing good news. I have just acquired the infamous Fireworks achievement (and it feels so goooood!
), and I am happy to report that this strategy did work for me. In the end I ran through Level 1-5 three times, getting the achievement at the end of that third run. Each of the Knights were kill purely with grenades and I even managed to get a couple of extra kills by destroying the 2 or 3 airborne soldiers halfway through the level.
I would like to add one disclaimer though. As I stated in my first post I have been trying to get this achievement for quite a few days so I'm not sure what my total "airborne kill count" was eventually. That means that these final runs may have just been enough to push my total over the edge as it has been suggested in other threads here that the actually total is far over the 10 mentioned in the achievement description. Not sure how relevant this is but it's something to keep in mind.
Anyway, I can at least confirm that this method works. The chapter isn't to long and the Knights are far easier to hit than their smaller, faster cousins, even if it does take a couple of grenades to bring one down.
Best of luck to everyone else try to get this most annoying of achievements. It's a real doozy.