I have a dog that was born in my house (she was born to a rescue about 3 weeks after I saved her) and she was a good two years old before she stopped chewing on things. I lost a pair of expensive brand new boots I never got to wear, numerous speaker sets because she chewed the wires, she chewed the cuffs of 3 different leather jackets and ruined them and countless other random items. I went the same route with sprays, yelling at her, catching her in the act and swatting her, confining her, you name it.
Regardless, I kept her and she is the most loving and loyal dog I have I think because I saved her life a couple of times and she realized it. She still carries small things around in her mouth, like small bottle caps she finds, or bits of paper, etc. but she no longer chews. I attribute it to simply growing up, because for her size and breed (16 lbs JRT/Chi), two is adult.
Be patient and keep trying. I would never give a dog up because of chewing, it's just like thumb sucking for human kids. Difficult to break but necessary, unless you want large bills- dental for kids, replacement of items for dogs, and sometimes you just have to deal with the bills anyway for the love of the kid or the dog.
Oh, and walking her at least a couple of times a day will probably help.
It seems to me you're looking for a quick fix instead of using preventative measures to address the real problem. First off, your dog needs way more exercise. A tired dog is a happy dog!
Taking him on more walks (or doing agility, playing fetch, frisbee...) will really cut his energy level so he'll be more manageable. You said it yourself--he's a very intelligent dog. That's your problem!
You can't have a smart dog and assume it'll be happy doing nothing. He's chewing everything in sight because he's bored (imagine being a 12-year-old kid in a class with 4-year-olds; you'd be bored out of your mind, right?). In addition to more exercise, you need to provide interactive/enrichment toys such as Kongs stuffed with treats, Everlasting Treat Balls, Hide-a-Bees, puzzle toys... That way your dog will be busy figuring out how to get treats or toys out of fun toys and won't want to chew your belongings so much.
You can also train him more--there's no limit to what dogs can learn, and it'll be especially fun for him if he's as smart as you say he is. If he knows all the basics already, then teach him how to retrieve things (like the remote control, your slippers or shoes...), or how to do dance moves, anything! You also need to set your dog up for success; when you're not home, put him in a crate with some fun toys to keep him busy.
When you are home, use a leash to tether him to you so you can see what he's doing at all times. That way if he tries to chew something in your presence, you can catch him in the act and trade out the object for a chew toy. This will be a lot of work, but if you love your dog these are the measures you should take.
If you don't feel that you can provide the exercise, supervision, enrichment opportunities, and training for your intelligent dog, then yes--you should surrender him to a no-kill shelter or pet rescue.
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