My dog would eat the kong toy to get the treat out.... so he usually gets a huge rawhide bone to chew on, but he slobbers so much, it gets all soft and gross. I cant remember at the moment, but there are a few toys at petsmart that are made of super tough but a little pliable rubber that stand up to chewing really well...
Also, check the back of the science diet and read the ingredients. If you see cornmeal or corn gluten or any type of gluten in the first few ingredients, it means you are basically feeding your dog sugar, which doesn't satisfy some dogs (nor is healthy for them). Science diet is sold mainly because vets get incentives to push it. Doesn't mean it's any good. The debate is still up in the air over this, and some people have dogs that live to 20 years eating kibble's and bits. Just an opinion.
Well, it sounds like you do care for your dog, but at the same time I do have a few sugestions for you as to what may help.
First off, get a lid on the garbage can. It will help hide the food your throwing away and even though he can technically smell it, he won't be as tempted.
Secondly, why not change up his food a bit? You can still feed him Science Diet if you care too, but try adding some of this: Natural Balance Dog Food Rolls. It is an semi moist food in a roll, completely balanced nutrition (so it technically would be able to be his food) but what I like to do is cut off a slice of it (they have lines of where to cut) and crumble it in my dogs food. You will notice that they think of it as almost it was a treat, but it is completely dog food, in a large roll and best part is that it doesn't contain a lot of water so you are actually paying for food, not water like in can dog foods. Best of all dogs love it. Feed it to them mix in their food 2-3 times a day. Give them 10-15 min. to eat and also make sure you don't free feed (unless you know you are not going to be home or plan on going somewhere), pick up the food after the 10-15 min. you let your dog eat, even if he hasn't finished it. This makes him realize that he eats when you eat. And he won't be as tempted to go into the garbage.
btw it is ok if your dog is not eating as much if you are splitting his meals up more frequently throughout the day, it's also better for you dog to do that.
also as for things for your dogs to chew on that would be safe for him, I would recomend trying some Cow Hooves ( you can buy them at pet stores or online at Petedge.com would probably be cheaper for larger quantity), but just make sure you watch your dog the first time he eats them, some dog's who have sencitive stomachs can't handle them. Also I would recomend if you are doing any training for him to stay out of the garbage can, try using freeze dried liver treats. They normally cost a wee bit more in the store but well worth it! Lots of dogs will do anything for them!
As far as good chewing toys,...it's hard to say what is good for everydog. For the dogs that love the Kong toys, that's great, but I know not all dogs want to chew on the ruber know matter what kind of cookie you put inside. I still recomend trying a kong but maybe trying to freeze penut butter inside of it or dip it in beef broth so that the dog will be more willing to chew on it having it taste more like a bone than rubber. Otherwise there is always a good assortments of Lamb and pig ears and snouts that will help crave a chewer so they won't get into trouble.
If at all else maybe provide him with more of a task type toy such as a ball he must roll so far to drop out a treat for him, or those hide a squirrel toys which make your dog have to "find something" and have a task at had to keep him busy.
If anyone else has any questions about dogs feel free to send me a message! I will be more than happy to help you with it! I will answer questions about Dogs, Cats, birds and small animals. Feel free to ask, I enjoy helping others! =)P