Cat Health Questions? Ask a Cat Vet for Answers ASAP.
I wish this behavior was better understood. Most cats gravitate to the litter box because their instinct is to bury their waste. Why some cats like the feel of the sink or bathtub does not seem to be reflected in wild cat habitats, but it just happens. If it were urinary accidents or diarrhea, we would at least consider a "health" issue rather than behavior. But if these are normally formed stools, then it's almost assuredly behavioral.
This leaves us with cat training, which while frustrating, can be accomplished. Training, as in dogs, involves negative consequences to unwanted behaviors along with praising. Cats are often less food motivated, but if your guy likes treats, you can try to be attentive to when he does successfully use the litter box and reward him. Likewise any other treat catnip, a hug, etc... can help make using the box a "good" thing.
As far as trying to prevent the use of tub and sinks we can work on two scenerios. Have a handy spray bottle of water or a can filled with coins or pebbles to shake or an air horn or whistle... handy near the bathroom so if you catch him in the act, you can provide negative stimuli. Obviously we don't want to throw things or hurt him. It is also better to have one of these "neutral" devices to provide the consequences so that he doesn't as much resent you for punishing, but simply associates this unwanted behavior with a noise or spray of water which he won't like. Consistency is always key in training, so it might mean camping out around the bathroom or stalking him a bit to try and ensure he gets caught in the act as soon as possible so the training can begin.
There is also room to try booby trapping the sinks and tub so that he will not want to use them. Scat Mats provide a mild static discharge and are used on furniture, counters, and could be placed on sink/tub. Please be careful since obviously mixing any electrical device with water is dangerous. Maybe even putting one at the threshold of the door to the bathroom could be tried. Another option would be leaving the tub and sink partially full of water during the training period. It won't take too many leaps into the tub with a few inches of water to hopefully change his mind. Obviously we only want shallow water. Drowning is not an appropriate correction.
Finally, there are drugs that can be used to help relax a cat who is showing behavior problems such as inappropriate eliminations. Pills to help reduce anxiety can be prescribed by your vet and phermone dispensers (they are like a Glade plug-in) can be put around the house to discharge relaxing facial phermones to help with anxiety. The logic behind this is that while your cat may seem very happy, there may be periods where his instinctive territorial/dominant behavior is coming through. As cats mature, we get to see their "true" colors and this may be more than just a bad behavior but could actually be the tip of a psychological iceburg.
I'd definitely focus on behaviorial techniques first, and the phermone dispenser is called Feliway and can be found at pet stores and some veterinary offices if you get to that point.