Hi all, am having the same issues here; I am the 3rd or 4th home for my 4 year old Savannah, and while he uses his box to poop, he pees anywhere but... he was already declawed in front when I got him, and though he is fixed, he will pee on anything, anywhere, anytime... I dislike the idea of adding a second box, especially when it seems like it would be for nothing; I suppose there must be scent lingering from previous residents, which is complicated by the fact of wall to wall carpeting... I can't put up with the stench any longer, and the most ardent cat lovers I know say they wouldn't keep such a cat, but he is so loving and such a baby that it would be a shame to have to get rid of him... people say that fixed cats don't spray, well this one does... sigh.
Nobody would want to live with the stench, BUT generally it is resolvable with some work. The first thing to establish is if your cat is healthy, a urinary tract infection can start this. Paw pain can start this, you mention the declaw so you should have his paws examined to make sure this isn't an issue. We had a Rescue kitty with this issue, and surgery to repair her paws and she's been perfect ever since. AND she is a much happier loving kitty as the pain was making her very very cranky.
So you don't mention how long you have had your cat, other pets, and what litter you use.
Best is to try the second box, but also try Cat Attract litter. Not only does this have an additive in it that attracts cats to pee in it, but it has a super-fine texture that cats like and is more comfortable to declawed cats.
The location can be important too... as can the box. The box needs to be large, and some cats really don't like hoods/lids nor do all tolerate an automated box.
if you think there is lingering scent from other cats, that might well have triggered the behavior as if the poor cat is on his 3rd or 4th home you can imagine he might be a tad insecure. Carpet is terrible for retaining odors... so I would suggest renting a carpet steam cleaner and instead of putting in the normal cleaner, put in Anti Icky Poo or Unique Distributors Odor Eliminator. If you find certain locations have been peed on more thoroughly, consider the injection thingy they have on the Anti Icky Poo website. I've also soaked an area in the Unique Distributors enzyme cleaner then covered the area with warm damp towels overnight before removing and allowing to air dry. It was really helpful (the product instructions suggested this).
Are you sure it is spraying or is it peeing outside the box. Spraying would be backing up to a vertical surface rather than peeing on the carpet for example.