re: Zoysia grass growing in clumps

Are there uneven spots/divots in the yard that allow those spots/divots to get cut higher from the root than other areas? That may be the cause of the runner stems going vertical and the blades growing out of them at an elevated starting point. In other words, in most areas those runners are growing horizontal/flat, but are growing vertical/up in some places, presumably from a higher cut point. I don't see a thatch problem in your pics, although de-thatching would invariably thin that out. But I think periodic scalping down really low may be the only way to stop that. As long as those runner/stems exist, that's the starting point for growth.