I know dogs and cats are different, but can I try and help anyways?
We always use Febreze or Renuzit liquid sprays when someone has an accident or throws up. I've never tried Nature's Miracle or any of those products, so I don't know how Febreze or Renuzit compare, but they seem to help get rid of the smell when our dogs have accidents.
I hope you find something that works. Our rescue/foster cat, Sebastian, has a bad habit of not trying to cover up anything that he does in the litter box, so I can understand wanting to get rid of the smell.