Don't do it, especially in spring. You mentioned steep hills, a problematical factor.
Potentially you could kill zoysia with glyphosate, Strip it with a sod cutter, resod with Kentucky bluegrass.
If it is steep, the sod removal with a machine will be tricky. And the labor to pick up sod rolls with wheelbarrow will be high. The new sod will have to have wooden stakes to keep it from sliding down hill during rain.
If you try to seed--you may have soil erosion during heavy rains.