I feel for you, Lesa!
I was out in my smaller veggie garden today, weeding the paths. Practically every weed imaginable finds that garden! Two of the worse are quack grass and lawn grass. I have eliminated quack grass from everywhere but along the border with the neighbor. It just keep creeping in there . . .
The lawn grass (KBG) must be my own fault. All I can figure is that I track the seed into the garden. It would carpet the paths nearest the lawn in a single season. Then, I'm sure, it would take over the remainder of the garden paths in another year. That might be fine if it could be trusted to stay in the paths but I know that that grass has other ideas.
My preferred technique for weeding the paths, and it is particularly appropriate for the grass, is to show up about 24 hours after I've run the sprinklers. I go over the path first with a spading fork and next with the 4-prong cultivator. I use that worn-out, short-in-the-tooth cultivator from the picture I showed you a few weeks ago

. The idea is that I'm not really doing any digging with it - the spading fork did that. The cultivator just "flicks" the weed out of the ground. (Then maybe I have to "bash" it a couple of times to knock the soil off the roots

.)
BTW - if the soil is good and damp, I don't really have to step on the spading fork at all. A couple inches is all the depth I'm trying for.
This approach might work for you . . .
Steve