We typically blow it till there's little left but the runners, then pull them out by hand. It isn't a satisfying solution, but it's the best I've come up with. Air spading is rarely a turn-on-the-machine-and-go operation. You blow awhile, get in with hand tools awhile (to pull out loose rocks, cut out problem roots, and, yes, pull out grass or other plants that are in the way), then repeat.
This is a great technique and vital to our industry, as most trees that have been planted in the past few decades are going to have root problems resulting from poor nursery practices and incorrect planting (not to mention fill on construction sites). But it's lousy work that is best handed off to the groundie, if possible. That's my position on it, anyway.
k