Yes this was more or less the path I was taking (someone posted up a route on Reddit I think - I found it via google): start at Ruins of Abyd, backtrack a little at first as there is a tomb/lower spawn point, then basically follow the path right up to Tomb of Eldritch Sun, checking the tombs along the way.
But the problem is that he also has a chance to spawn in Sunward Spire (as you describe). On most of my runs, by the time I was getting to Tomb of Eldritch Sun, he hadn’t spawned, so I had to take a detour into the Sunward Spire, which is v. time consuming, as the mobs are so thick you can hardly run past them. And he spawned in here a few times for me!
I probably need to work at refining my runs, and only practice makes perfect. I wonder if there is a spot where he has more chance to spawn, and therefore it would be more time efficient to just check there each time, and reset the game whether you find him there or not?
EDIT: anyway, SR is pretty tough, so I think it’d be good if he at least had a chance to drop it, considering how rare it is to get a good prefix and suffix anyway. Maybe a reduced chance to drop compared to the main campaign?
EDIT 2: also, do you farm him on ultimate or on lower difficulties?