I used to ride a TB with I believe a somewhat similar shape. We rode in an older prestige… I think in a MW that we then used a shim pad, shimmed at the withers, to fit him in the front. I.e., he needed the width in the back, but not in the front. I believe that used to be a fairly standard approach for TBs. Not sure if it is any longer. Also, that saddle always put me in a chair seat.
For all the people recommending Black Country, believe them! That’s what I have now, although not for a TB. Wonderful saddles and lots of options.
Also, you thought Custom might not work. They do have a curvy tree in the Icon Star. I test rode a horse in one who had a very steep drop right behind the withers and it fit well. Personally, I hated the saddle because the rise in front was super steep, but you might like it. It seemed like everyone else liked that saddle except me.