Fiona
You are going to struggle with this I am afraid. Repeated urine on a porous stone by cats

You are going to need something a bit more effective than Talcum Powder and Hydrogen Peroxide.
There are several problems here that need to be solved.
We not only have urine that has probably not only penetrated pretty deep and caused an unpleasant aroma but it may have acid etched the stone as well. So the urine could have etched its way into the stone probably in dozens of places if the stone is acid sensitive.
My first course of action would be hone the floor using an aggressive 60 grit honing powder and a Tynex brush. This will break up the stone surface , change the surface tension and make the stone more porous. I would then rinse with boiling water and extract with a wet vacuum.
Next I would then use Miracle Liquid Poultice Parts A & B. Part B acts as an Oxygenation agent (Bit like the peroxide you proposed) only a lot more aggressive.
Here are the instructions for use:
Thoroughly mix 1 part of Liquid Poultice(Bottle A)with 2 parts hot water. Add 1 part
Activator (Bottle B) to the above mixture. Once the Activator is added, be sure to keep the mixture vented to prevent oxygen build up. Mix in an open container. Once Activator (Bottle B) has been added, the solution must be used within 72 hours.
Wet the surface to be cleaned with water lightly before starting.
Apply Liquid Poultice with a clean mop, or direct from the tank of your Mono Rotary. Allow the solution to stand for a minimum of 45 minutes while agitating periodically with the appropriate scrub brush. DO NOT allow solution to dry on the surface. If surface starts to dry, add more Liquid Poultice Solution. Extract all the dirty remains with a wet vacuum system. Rinse the surface thoroughly with hot water and allow to dry. Difficult stains may require a second application. On wall surfaces a fine mist of Liquid Poultice maybe left to dry after initial cleaning is complete. Liquid Poultice will continue to pull dirt to the surface for up to 72 hours after completion. Allow to dry 24 - 72 hours before sealing the surface.
Kev Martin
Marblelife Ltd