I really doubt something like fluoxetine would work for your dog. Discuss it with your vet, or better yet, a veterinary behaviorist (be VERY careful finding a trainer who calls themselves a behaviorist.. I would be happy to elaborate on this if you're interested) to find a treatment method that would work.
But here are my thoughts.
It sounds like the dog is very mouthy and gets a lot out of oral stimulation. Some dogs are just like this. It's no different than some dogs being obsessed with balls, or pacing the yard, or jumping. It's a vice, and obviously on the extreme end of the spectrum, but no different than other doggy vices.
It also sounds like he may be lacking stimulation in other areas that he makes up for with the oral fixation. Like physical exercise. I realize at 11 years old it might be difficult to tire him to exhaustion, which brings me to my next point.
He would probably benefit really well having a dog proofed area where his oral needs can be met in a safe way. A place like a gated kitchen, laundry room, foyer, or someplace with bare floors where it can be just him, some chew stuff, and a stainless steel bowl of water.
Also, I am not against re-homing dogs IF the dog is in the physical and mental state to transition well, AND, if the home he's going to is better suited to meeting the needs that are not being met in his current home. If the latter can't be found, you're essentially bouncing him, which is unfair and irresponsible. If you can find a home that meets those criteria, it might better for all involved. However, he's 11. There's a good chance it could be mildly stressful, which could just cause him to relying even more on the satisfaction of chewing.
At this point you should resign yourself to supervising this dog 100% of time (and by that I mean within a few feet of the dog, not distracted by computers or kids or phones.. eyes on the dog and the dog only), or creating a safe area where he has access to NOTHING that is chewable. A lot of people feel like "meanies" for gating their beloved dog in the kitchen all day when the dog is used to having full access to the house, but I think it would be the lesser of all evils, and a lot easier to get used to than a new home.
Have you considered feeding him a raw diet? You'd be able to customize his diet to include a lot of chewing (bones). You could feed several small meals a day to offer lots of opportunities to chew. Although at his age he may not take to a raw diet easily, which could also be frustrating.
And lastly, you could try a basket muzzle. They can still drink water, but with a fine mesh he'd be unable to chew (or not chew as much). He'd still be able to run the house, but most objects wouldn't be chewable (though sometimes they can small objects through the wires, hence finding a fine mesh style).
I think a gated safe area would be your best full proof plan though.
