Zoysia turf loses even more water when it is too tall. Also, the thatch build up caused by keeping the grass too high will keep water from going down to the roots, it all hangs up at the surface. Now if this is in a non irrigated lawn, forget it. The appropriate turf is Astroturf. I do not know of grasses that look good with less than an inch of water per week for more than 2 weeks consecutively.
As I said, if you are able to cut low enough, the material removed is what is causing the trouble. Well maintained zoysia lawns in Hawaii do get cut down at scalp heights when they are thatchy or uneven. The scalp and bag sounds good to me. One more thing, when zoysia is Verticut, recovery from that procedure can be very slow.
The norm here is for sodded lawns to have their seams filled with sand right after they are laid. That is what is expected of the installer if there are any gaps between the pieces. Yet one more reason why sod is not less than $1 installed here. The standards are different. For a reel cut lawn, the sand needs to be washed in with a hose and your first cuts need to be high enough not to touch the sand.
They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety.
Benjamin Franklin 1775
Sell not virtue to purchase wealth, nor Liberty to purchase power.
Benjamin Franklin Poor Richard's Almanac1738