My guess is that your v-bit does not come to a true point. That will cause the carves to be wider than calculated at your desired depth. You’ll have to set your Z0 at an offset above the surface of the wood. The offset depends on the width of the flat spot on your bit. With a 60 degree bit, you should be close by offsetting the slightly less than width of the flat. For exact offset, I whipped up a basic spreadsheet you can enter your values to get an offset.
That said, raise your zero and just run a couple of tests.