Ottawa, This is going to sound silly, but I suggest you go buy a HUGE flat under the bed shallow container, so huge there really isnt any excuse to not use it. Perhaps you can get a free one from a family member or friend. I suggest this because our Siamese rescue cat had issues with a normal size pan, we had to get a very large one, not as big as what I am suggesting you try. I never did get the perfect solution for our dearly departed siamese and had I thought of the huge size of those roll under the bed storage trays, I think she would have been happy. Sounds like your basement has plenty of room.
Ironically our Maine Coon kitten, who at six months already weighs more than her prefers a snuggly lidded cat pan, so its not the size its just what their silly feline mind thinks will make the perfect potty!
Our new member of the household is Leonidas, aka man chin (nicknamed because of his pointy cleft chin) he should mature to around 20 lbs, but right now he is a rangy long guy with a HUGE duster of a tail.
So far we've stuck with the same food/kitty litter as he used as a kitten. The food is IAMs kitten and Friskies canned (.46 at walmart). Leonidas is a fan of dry food and only eats the wet sparingly. I want him eat wet food for the water content and to keep his coat healthy, not dry. The kitty litter is insanely expensive, but it works well, it is World's Best.
If you like to have your cat wear a collar, you can buy handmade ones from Ebay for $1.50 to $3.50 each. I bought a variety because the price was so cheap, shipping was combined, $2 for the lot of them.