That's a lot of poles!! It's basically down to 2 things; 1 something is wrong medically, how old is the horse? Where was the stiffness? Have a full workup from the vet, if they find something there's your answer. If not horse is not a jumper, you can try and improve but can't turn them into something they're not unfortunately. Grids, a frames, sold fences can all help but to be honest a horse that has that many poles in 2 rounds I really doubt it'll improve enough, you've already said grids haven't helped. I'd also worry about taking a horse over solid fences that was having that many poles down could end up having a accident if it leaves a leg behind XC.
Does sound like too much jumping but from experience I usually find horses that have gone sour refuse to jump rather than just hit everything.
Doesn't sound like the horse is either capable or willing to do BE, maybe time to either get a horse that is suitable for the job or change what you want to do to fit the horse.