I second Neiderseuss for the big shoulders; there’s big shoulders, then there’s the crazy, trapezoid-like shoulders where they just keep getting wider and wider from the base…
I have this exact horse. He is a TB but you wouldn’t know it looking at him - he is dense & thick as TBs come, with a big wither and his shoulders… god. They’re huge. Anyway, I rode him in an Ainsley Chester XC for a while and while it fit all my past TBs, it wasn’t a good match for him: the tree points in Ainsleys go straight down rather than fan out, and it made his shoulders sore (it was fitted to him too). I played around a little, pulled out an old Kieffer Wein dressage saddle; the trees in the Kieffer point out a little more and it was much more accommodating for his shoulders.
I ended up purchasing a Stubben Zaria with the New Tree (NT); it has made an incredible difference. The tree points in the NT angle out on a curve, which is exactly what a horse like him needs. No complaints. He loves, loves, loves the saddle. Goes much better in it than anything else.
I was having a hard time justifying the cost, until I cantered him in it… He was a pretty green OTTB at the time, but that canter sold me - it was completely different than his canter in all other saddles.
I’ve had really good luck with Stubbens on TBs in the past: I never get the “stereotypical” TB - mine always seem to look like some other breed over a TB be it QH or Cleveland Bay… so I’ve got a collection of saddles that work well with them. I’d start looking at Kieffers and Stubbens and go from there.
I would personally avoid most french saddles if I were you: I found the panels are too round for most TB backs, which tend to be a little flat and broad… At least my TBs, anyway.