You might consider an atomizer to apply the Roundup with. Someone in the lawn maintenance field could probably answer the question better. But when I built my house, by the time I was ready to put in my lawn, there were weeds everywhere and they were a good 2' - 3' tall. I had hired a landscaper (my secretaries husband) to help design our landscaping and to take care of the initial creation of the planting beds, sidewalks, etc. He came in one day with a walk behind push type atomizer. He said he was using roundup, and he walked back and forth just like you would with a broadcast spreader. I remember asking him if the thing was working, because I couldn't see anything coming out. He said it was working just fine.
Two or three days later, every weed in the yard was dead. As far as I know, he used the regular Roundup concentrate, but with the atomizer, it goes a lot farther.