What if you got a certain number of attractions and then that was it. Like, you'd book two or three attractions for the day, but you could never add more. That way there would at least be less burden on the system and there would be somewhat less pressure to game it to get as many attractions as possible. And you wouldn't have to sit on your phone all day. In fact, you could feasibly manage without a phone if you were able to make the reservations the day before.
Of course I understand that people would still want the E-ticket rides (which not everyone can have) and that would be stressful. Maybe you could do tiers where you only get one headliner ride. I'm just trying to think outside of the tired "they need to limit sales" idea here. Instead of limiting the number of people who get to ride whatever they want all day, where everyone else is a loser, you limit the number of things that everyone can ride all day. A different way to manage the lack of capacity, horizontal rather than vertical as it were.
I'm also leaving out the issue of cost. I'd prefer it be free to maintain the character of Disney as a friendly and different park, and also to cut down on complaints when people can't get whatever specific ride they want. But presumably there could be a (fairly low) charge.