I would argue that just having a kanban board during stand-up meetings and "walking the board" instead of interrogation-like status reporting is going to do wonders to team collaboration atmosphere, morale and actual productivity.
You start to see and talk about the flow of value, what's next, what's in the moment ("what can we do right now?). You see context. All of that is missing with SCRUM or only possible with a highly motivated and responsible team that communicates a lot automatically.
I'm not yet saying that kanban is solving the software crisis [1] but it turned around quite a few teams that I've seen and been part of.
DISCLAIMER: I'm working on https://www.blossom.io which is a lightweight kanban board.