Zoysia Grass-any advice is appreciated

So my wife and I bought a house and whoever laid the sod did not level the dirt before. I have some areas so thick that I cannot cut it with a gas or reel mower. Some areas seem to never grow-they are green, just very flat. I there anything I could do to avoid another summer of having to trim the entire yard because I cannot cut it? Should I get a mower and hack the dead thick parts down now? Should I de thatch the thick parts? Any help is really appreciated. Thanks.