Sorry to hear that you have this problem. We have not had a camera down our drains, but we are pretty sure that we had some construction debris put down the drain that tends to snag other things. No amount of "snaking" ever got anything up though. I think your plan is at least worth a try. It is not expensive to use the mainline cleaner, and if it solves the problem, that would be great. A new toilet would be more expensive, but I think you are right that one bigger flush might be enough. However, the point of flushing twice might be just to make sure everything has moved down the drain. I think you probably only need to do that when someone has a bowel movement, which would only be a few times each day. Another possibility is to put your toilet paper into a covered trash can, at least most of the time. They do that in China to prevent drain problems. It isn't common here, and you probably wouldn't want to ask visitors to do that, but you could try to see if that helps.