I buy the cheapest high N, K, w/Iron I can find. I can't afford Milorganite
The best time to fertilize is early-mid December so that the Zoysia is green and healthy all Winter and thru April.
It takes a bit of work to keep a nice Zoysia lawn in this climate. You should scalp the lawn (1") during rain season to get rid of the heavy Zoysia thatch layer every year.