I used to mix baking soda in the clumping litter about 14 years ago, and it did help somewhat. But I did find I was using a fair amount of it at the time with two cats. I ended up buying the baking soda at the farmers feed store in a 50 pound bag it was the cheapest, because it was meant for cattle feed and not for human consumption. I know at the time a lot of people were using baking soda with the litter, to help kill the smell of urine and I don't recall any ill effects from it.
A few years ago, when Swheat Scoop was relatively new on the market I switched over to it because I thought it would be healthier for the cats, and it appeared to be a bit cheaper. I now have five cats and a 40 pound bag of Swheat Scoop will last me a little over a month by a few days. The price of a bag is about $35.01 including tax. And when you divide that between five cats it comes out about seven dollars a month per cat. I don't know how that would compare with today's price on clumping litter, but a 40 pound bag of Swheat Scoop should do you about five months. They do make it in smaller bags, but I haven't done the calculations to see what it would come to cost wise.
I haven't tried either the corn-based or the pine litters. So I can't give you any breakdown on them, but I do know they come highly recommended by those people who use them, and when using these litters the, oder is nonexistent. What I like about these litters is you can flush them or you can add them to the compost in the backyard. Unless you are on a septic system then I wouldn't advise flushing.
As mentioned by "14+ kitties" above, the clay litters pose quite a hazard. They will swell up to 20 times their size when wet, depending on the brands, so you can imagine what it would do inside a cat or dog if swallowed. It will really clog up the works, not to mention what the bentonite clay does to the landfill. Anyhow, check out your cost for clumping litter compared to mine and see what is the cheaper. You would have to go to the large bag of Swheat Scoop for a better price. I do know where you're coming from on the price, but I think you'd be a lot happier with some of the newer litters on the market. What would make it handy is if we had some feedback on the cost per month from other people and the type of litter used.
This will give you something to think about anyways. And if you do decide to change litter, make sure you read the instructions on the side of the bag on introducing your cat to the new letter.
Regards, your last post. I can't comment on the use of vinegar I haven't tried it. If the smell of the vinegar is too strong that could repel the cats from the litter area. Their noses are about 14 times more sensitive than ours to smell. Something that you should be aware of is air fresheners. Some of them carry essential oils and can be very detrimental to the cats health especially when used in a confined area. So if you're going to try and mask the smell make sure you've done some research into what you are using as a masking agent.