Can't it be controlled with a grass herbicide that can be applied over the top of broad leaf ornamentals? I'm asking because I am not familiar with this weed, but it is quite easy to spray grass weeds right in the middle of your ornamentals with the right product.

Poast and Select are two herbicides meant for grass, both are expensive. They work best on young grasses, 5 to 6 leaf stage. Older grasses, react more slowly (2 to 3 weeks). Once they begin to head out, forget it.
You could try wiping them with a mild solution (1%) of Round-up. Put on a latex glove with a cotton glove over top. Dip your hand in the solution and grab the leaves you can get at without dripping or touching your ornamentals then pull up. Try not to damage the leaves but get as much Round-up on the pest as you can. Again though, if the grass is mature, the results will be less than desirable.