I know you have already tried a few avenues, but it is not uncommon to have this mystery lameness and then after consulting a equine sports massage therapist to get some answers. Even a simple evaluation from an ESMT could likely help to pinpoint what is going on. 60% of your horses is weight is muscle. Their tendons are tight and can become torn when their muscles are tight. It is unfortunately that no one has mentioned this to you yet. For some reason equine bodywork is a somewhat ignored resource. Depending on where you are located I would think that an ESMT could come do a free eval for you.
It could be that he is incredibly tight or has some back issues. As for you seeing something wrong with his right front and hind left, if that is correct, it could very likely be muscular and could be greatly improved with massage, in the least it will be pinpointed. He may have a muscle injury in the either front or hind, which the horse will compensate for and usually manifest in the opposite diagonal.
A book that EVERY horse owner should have is Beating Muscle Injuries for Horses
by Jack Meagher - Hamilton Horse Associates, 1985. I highly recommend it.
Good luck and let us know how things go!