"The plant has a reputation as being particularly good at going to seed, even after being yanked out of the ground."

Turbo, yes it does and I'm afraid you missed your window of opportunity once the flowers appeared. Do read the other threads on this forum on garlic mustard.\

Sorry, wish I could be more positive.

This Nature Conservancy site might prove useful to provide options.

Here is a link that might be useful: TNC Garlic Mustard Management

Its not too late to remove the standing seed crop as the plants don't drop the seeds till midsummer.Yank the plants with their unopen pods and collect them into tight piles. Try to get them all from the area you are trying to clear,and remember try not to disturb the native plants in the same area as they will prevent the garlic mustard from recolonizing.Seeds will have to be collect for a few seguential years to totaly erraticate GM from an area.

What I've been doing is yanking the stuff out of the ground and chucking it on my burn pile (which due to burn bans here is now about 10' tall). It'll be hot enough to destroy the seeds, particularly since the pile is chock full of black locust wood.

Once the seeds emerge, however, I'll have to bag them to avoid drops all over the place.

Next year I'll do select spraying on denser areas of 1st year rosettes. I mistook them for wild ginger or violets, and let them get away from me.

...horrible, horrible plant...