Grumpy cat

I have two older cats. One is 10yrs, and the other is 12yrs old. My female cat, Jiji is 10yrs and is always in good health, had great mobility, and doesn't seem to have aged a day. My male cat named Doctor House Cat, he is 12yrs old (going to be 13yrs in May) has been having increasing issues with arthritic pain. He spends almost all day laying at the top of the stairs and watching everyone down stairs and rarely comes down.  Recently my husband and I moved from a single floor, to a two floor house, and I thought Dr. House Cat was staying up stairs at first  due to it being a new home, and he was just being anxious (very unlike him), but now I've realized it's due to pain when I heard him whining when he was walking (waddling) down the stairs, and I didn't realize how bad he was hurting. He's taken to fighting with his friends, my service dog, and my other cat, and generally being cantankerous (so unlike him). 
Do you have any recommendations for what I can give him supplement wise? I'm trying not to give him anything hard as he has a sensitive stomach. The vet simply told me that unless I want to give him pain medications he's probably going to keep having issues, but I'm willing to at least make him a little more comfortable. 
My husband and I are both concerned. Any recommendations.

PS: He is not overweight, but he has always been a very large cat at 20lbs. 

I would not use any supplements without the guidance of a vet.

You can try Cosequin, but not sure it will help much if he's in that much pain.  The next step up is sometimes Dasequin, both of these are supplements that can be sprinkled on their food and are similar to glocosamine for us humans.  Some people give their cats Krill Oil with good results, or even ground chicken feet, which are full of collagen. 

Other than that, you can get prescription pain killers from your Vet specifically for arthritis.  That may be your best bet at this stage.