You may as well plug it between the bermuda. Zoysia is well known as a s-l-o-w spreading grass.

You have a different variety of zoysia than I had (years ago). What I found was that when the zoysia got set back, the bermuda was very quick to move in and take over. Then the zoysia would recover (usually the next spring), and make slow inroads again. Until it got set back. We bought a house a year ago which seems to have an expanding patch of zoysia. The freeze took out everything, so we'll see what happens in March/April.