Adult Cat Litter issues

[kbbennet]

Hello all, new to the forum! I know there is a thread on litter training but I would like some fresh opinions. I recently just adopted two cats from our local shelter and now we have three wonderful Tuxedo kitties! They are awesome and all three have their own unique personalities. Recently, however, I've noticed that one of my new additions, Ozzie, is going outside of the litter box. In fact, he is going right NEXT to the litter box. Furthermore, he is not "missing his target". He is literally sniffing the area around the litter boxes (which have cardboard underneath), circling the area (much like how a dog does), and then squatting! Last night, he literally did this right in front of me while I watched his routine, no shame at all.
A little over two weeks ago, I noticed some staining on the cardboard and as of today, he has seemingly "marked" on all four sides of the litter area with both pee and poop. I added a third litter box (now three cats have three boxes). However, he still seems to insist on going outside of the box, more often, with pee. A couple of details:
1. Just moved into this home less than a month ago
2. Just bought a third box about a month ago
3. We use two types of litter and mix the two. Both are clumping litter. The first one, is the Arm & Hammer Odor Control stuff that is more expensive and is the main substrate in the boxes. The second is a supplemental to fill the box and is just a meijer brand, fine grain, clumping odor control version. Both types are recent changes.
4. I've failed to keep the box clean daily. I've been super busy working on our house and have left the box quite dirty lately. Just last night I cleaned all three boxes and the resulting waste bag weighed about 20 pounds, no kidding. But even after a thorough cleaning last night, there was a pile of poop outside of the box this morning!

Any ideas on the cause of this? He was adopted from a shelter and they reported no problems at all of him going outside of a litter box.

He stayed with my mom for a while and she reported that while she was cleaning the boxes once, he stopped, stared at her a minute, and then peed on her rug. I asked her how long she was cleaning the boxes and she said about 25 minutes. My guess was that he was upset that he didn't have his box for that long and he peed on her rug in defiance.

I need advice! I just bought new furniture and while he doesn't seem to be urinating or defecating anywhere else in the house other than next to the boxes, I don't want him to start taking this behavior elsewhere and/or prompting the two other cats to also adopt such behavior. Help!