@Pocket Pony I have a Welsh Cob that, like yours, isn’t barrel shaped. He’s wide, but has good withers and a decent front-to-back curve to his spine. What I’ve found is that there are entire brands that just don’t work for him based on front-to-back tree shape, and the symptom is that “popping” in the back you describe - it is NOT an “incorrect size” issue, it’s a fundamental shape issue. It’ll look perfect when he’s standing still, no bridging, great fit, and then when he starts moving it pops up in the back. (Also we only have this problem with Dressage saddles, he’s way easier to fit for jump).
I’ve tried multiple models/sizes/fits in the following brands and had the popping with all of them: Stubben, Prestige, Ideal, Albion, Wintec, Thorowgood, Amerigo. Then County and Devoucoux were okay but not perfect. The only two brands that have fit him perfectly without popping are Adam Ellis (multiple AE saddles fit beautifully) and CWD.
Good luck! I’ve been here for years and it’s frustrating. My Adam Ellis fit him perfectly but stopped fitting me after some position changes, so I’m currently waiting on a custom CWD to be made to the exact specifications of my absolutely perfect jump saddle that fits him so well. Pricey, but I was so tired of the revolving door of saddles that didn’t fit, it seems worth it at this point.