It doesn't sound like you need a better app. It sounds like you need better technique. You've described a lot of things that can be done in Trello, but many of these are doable in similar apps like Pivotal Tracker or Todoist. I use Sublime Text's extension PlainTasks, but that might not meet your 'low cognitive load' requirement. Trello/Kanban seems like a multiplayer checklist.
I'm not sure if it helps but maybe check out The Checklist Manifesto (https://www.amazon.com/Checklist-Manifesto-How-Things-Right/...)