I am not sure at all what your grassy weed
may be. When I have had to get rid of grasses in a field of a broad leaved plant like in a swatch of ivy, I have used Fusalade. It kills monocots without killing the other plants. But it would not be good in trying to kill off grasses in with other monocot-leaved plants like daylilies or iris' (that is anything with a sword-shaped leaf). And not good in a mixed planting of both types of plant leaves.
I hand pull/dig weeds
out of those kinds of beds. Hand pulling is the best if you are trying to grow organically. Or in amongst vegetables.