Well, for my answer, I am going to have to assume that the vet's assessment of him is correct and there is no medical condition. I cannot vouch for what urine test results came back.
1. Feliway therapy. Feliway is cat pheromone. You cannot smell it but can help with cat anxiety, stress, and has been used to help with inappopriate urination.
It is available in collars, plug-in the wall devices, and sprays.
2. Deterrants. Place something that prevents him from urinating in those areas. Classic examples are aluminum foil or double sided tape.
3. Diet change. There is a food called C/D Multi "stress" formula. This is really more for stress-induced cystitis (bladder problems) in cats. But, it "might" have some use in this situation.
4. Medication. There is behavior modifying medications that can also be quite successful to help as well.
A long read at the above link, but I thought you would like to have the information.
This last link above is the information about medications to help when all else fails.
Hope that information helps