Just get it over with. Tear out the carpet, seal the concrete floor, or pour acrylic sealant over the wood underfloor, then fill the room wall to wall with 3" of litter.
Then buy those Japanese wood shoes with the two slats underneath to wear around the house.
Only the ones where the OP is desirous of killing their nuisance.
Seriously, I own several animals. Some of them, I have a very high regard for.
The sooner you accept your cat’s overloardship, the happier you’ll be. What your cat is telling you is either the litter box stinks like piss and poop (duh) and you need to clean it better (swish some bleach around in it after you’ve scrubbed it) OR your cat hates your guts and wants you to hurry up and die a slow horrible death. Those dead mice it keeps bringing you, those are warnings, not gifts.
Now I’m picturing this…you might be onto something here!
Our cat Bob became an outdoor cat because of this behavior. He began to think outside the box, as it were.
He was happier, and we were much happier.