That's mostly what I use in my filters. The handfuls of oyster grit work, but they make a bit more of a mess if you don't have them in a bag. And I had bags of coral fingers and bits left over from when I had a marine.
Cats have a range of around 5 acres or so for domestic cats up to around hundreds of acres for feral cats. Stray/feral dog packs have home ranges getting up to 30,000 acres. For reference wolves can be up to around 3,000,000 acres
Cats can be walked just fine, you have to train them on a lead as a kitten just like you do with dogs.
Many cats will also fetch, they just have to learn. People have this self fulfilling idea that cats can't be taught anything so they don't try to teach them anything and then use that as proof that they can't be taught.
Yes, if you are desperately in need of a way to solve the problem of your tank setup being too cheap and simple then a calcium reactor would do the job.
But otherwise you're just adding extra complexity with the CO2 canisters and reaction chambers with it.
Solution: Don't let your damn pets or livestock roam. It's not that difficult. Any other animal you're required to keep under control, cats should not be any different.
Along the same line was at my father in laws on the weekend and he was angry at someone that's thrown oxygen weed(Elodea I think) in his pond. Only way now he'll be able to get rid of the infestation is to drain the pond, current plan is to get into the pond with his excavator and dig it out with the bucket but that's just temporary.