I hate to admit it, but over the years, I have applied enough Weed B Gone in the same areas that the distinctive smell is always there, yet, I still get weeds coming right back again!!!
When I lived in a subdivision, I always used Scott's weed-n-feed products for my front yard. Used a broadcast spreader, follow package directions. Nice, thick, weed free, dark green lawn that had to be cut every 4-5 days.
Your veronica almost kinda sounds like creeping charlie, except for the moist part.