This idea’s one of the features that are up next on the roadmap so it’ll be interesting to see how similar Monzo’s solution is to the one you’ve described 
@anon60556779 came up with these designs recently -
https://community.monzo.com/t/split-bill-splitting/6397?u=alexs
which Hugo said were similar to what they’ve been working on.
Most of the discussion of the feature happened here -