I have described the process a few times, this is one.
The key is having multiple objects.
The paint tool appears to be successful for ornaments, not this sort of model.
Make the disc a single solid colour after removing the paint you applied.
You can do this the same way you did with your text layer.
It also seems that you have not currently positioned the z -axis position, as it appears at least one layer too far up.
When you slice, use the right-side layer bar and drag it down to the first layer. If you see black, you are good, I suspect it will be white.
Read the linked answer to see more information.