Some 20 years ago we let our back yard die out during a drought, and just kept the front yard watered. When the rains finally returned, I replanted the back yard with plugs very much like you describe. I planted 2"-4" plugs every 12"-18".
It took the whole season to fill in, but your St. Augustine is a more aggressive spreader than the fine leaf grass we had. You should be doing well in 6-8 weeks.