I have some zoysia under trees in my yard. I wouldn't overseed it because I couldn't kill the ryegrass in late winter because the zoysia never goes completely dormant. No way I'd want ryegrass growing in my yard until June and that's how long it's going to grow unless you kill it with Gly in February.

If my people, who are called by my name, will humble themselves and pray and seek my face and turn from their wicked ways, then will I hear from heaven and will forgive their sin and will heal their land. 2 Chronicles 7:14