It sounds like you don't care about the spotty grass right there if the repair will fix it.

One, wait until late summer when you can reseed (and working on the lawn is so much more pleasant). Zoysia is a warm-season grass, so my timing might be off. I know cool-season grasses better.

Two, certainly you can use 1/4" of compost to add fertility to the soil. Can't hurt. However, the stuff decomposes into almost nothing after a while, so using it to fix your problem just means you'll have a problem again. Plan on using topsoil of the same consistency as what you have. Local suppliers can deliver enough for you.

Three, I'm willing to bet that the village seriously compacted that soil. A dense core aeration (running over several times with the machine) will help a lot. As long as you're sure the sewer line is deeper than the aerator goes (call it 4" to be on the safe side), which it probably is. Just be sure of that, please, or you're going to have a rather disgusting mess.

Four, reseed at the recommended rate (or plug with zoysia...I've seen plugs, I'm not sure of how successful a seeding is).

Five, roll it to get the seed in good contact with the soil.

Six, water three times a day until it sprouts (or the plugs adjust, in which case it may need less water).

Are there any zoysia experts out there who can give the correct timing for this?