Before you consider that final road, try this:

There is a pet form of SAMe...for smaller cats and dogs.
It is called Denosyl and is 90 mg/tablet.
Human SAMe is 200mg/tablet

This is a very good natural intervention. I have met people with large dogs with
hip dysplasia where it worked well.

You can ask your vet about it and get the dose you'd need for your dog.
It is available on line for somewhat less than vets charge. I used it for my cat.
Human SAMe is less expensive if a 200mg size is appropriate.
You cannot break the tablet up and mix with food, it has to go down whole.

I even met a Rottie on vacation one year who used it!

It has the added bonus of improving mood and attitude as well. Pain can make pets depressed. My cat really responded to it positively.

Good luck.