The training covered not only the time and place, but also covered the details of toxicity. A quantity of 2-4D that would be about the same as a roll of life savers rubbed on the skin of four kindergarten children would kill two of them. This is not getting it in their mouth, but just rubbed on their skin. My reading on this subject has exposed spreader far too many nightmares than I care to share here. Now that you aren’t dumping toxic gick on your lawn, you can enhance it with some other growth. The above methods will prevent dandelions from propogating. Since dandelions live about five years, the mature dandelions will struggle with the tall, thick turf and die off in two to three years.
I’m not very familiar with warm season grasses to make a recommendation. It could be two weeks until you see the baby grasses. In the meantime, weed seeds have probably germinated. It stands up well how to regrow grass to the abuse of football games and pets. It will also stand proud at three inches, four inches and five inches! Before my master gardener training I thought that herbicide use had a time and place.