Has your doctor done a pouchoscopy? That might help narrow this down. The Augmentin timing sure suggests pouchitis, and it might be worth trying a different pouchitis med, like rifaximin. I found that psyllium capsules didn’t work well for me (they didn’t mix properly), but the powder does the job well. And I do suggest you try a much higher (10-20x) probiotic dose for a couple of weeks at least.
Do you have a gastroenterologist? A good one is sometimes more helpful than a surgeon. Good luck!