If you continue mowing it short, how will the burnt-out areas recover? I suggest getting a used 21" push mower from a pawn shop or Craigslist.com. It'll run you $25 - $50. This will let you mow tall for the time being. Grub control can be had at your local garden center. Forget the soap/water thing. Also, do a split-app of the pre-emergent. One in late September and one in late winter.