Lot of great ideas. The problem I see is execution (I'm an ex-employee). Primitive versions of most of the ideas suggested in these comments are tried and given up because they didnt really show huge difference in growth or other engagement numbers - This is partly because one of the below:
1) primitive implementation/design is very bad compared to the original idea.
2) There is huge reward in Twitter for starting new projects. But no one follows through to make sure project is well maintained/supported.
3) Cross team coordination is not good