Let me perhaps challenge one supposition, this notion of incremental change.
Parliament has been studying this thing for 95 years. We don't do this very often, if ever. We have this moment in front of us. My brief time in Parliament has shown me that when there are moments, there are moments, and they can flitter away like the attention span of a gnat in the way things come up and go down, and Twitter has made it worse.
Why not go for a proportional system, even a proportional system that you've suggested, modified so that the counting is not done by first past the post but in a modified way?