I had asked for some clarification of the post and have not heard back. However I can address the questions about something beyond the Motrin or Naproxen.
There are several options to consider in this situation.
First, it is an option to consider a different anti-inflammatory medicine, several of which are available by prescription. It is not that another anti-inflammatory is "stronger" than Motrin or Naproxen, but instead that different anti-inflammatory medicines work better for different people.
Since you do not want to take anything that is addictive, that would exclude the use of opiates.
Another option, though, would be to use medicines that suppress the firing of the nerves that carry the pain message. The most commonly used medicines are certain anticonvulsants, such as gabapentin or pregabalin. Certain antidepressants also have been shown to help relieve chronic pain, including amitriptyline or duloxetine.
You asked in a separate question specifically about supplements. There are no supplements that are as effective as what I noted above. However, turmeric may help with inflammation. Glucosamine and chondroitin also may help with degenerative arthritis.
If I can provide any additional information, please let me know.