I am not a sod expert, but if you and your neighbors are all having trouble back there, it could be that the earth is more compacted in that area, impeding the underground spread of the zoysia.
If so, aeration might be of help.
My neighbor tells me zoysia is seed now available and although rather expensive, she is having good luck over-seeding with it in sparse spots.
Perhaps that combo would give better, lasting results than another chemical would provide.
Should you try it, (I would) hand pick the shallow rooted weeds until the seed fills in.
