Hi there, I'm not 100% sure on what else to look for, but I'd look away from the flexplate for now, when that is nearing end of it's life you get rattling/rasping noise mainly at idle or not at load. I had an almost failed flexplate and wrote quite a bit up about it if you need more info, but I can't see how that would cause you a P0344 or hesitation as it's a solid metal wheel, it'll either work or totally give way and won't transfer any movement from the engine to gearbox.