I generally agree with you — I do not assume have found The Fix for Twitter!
My suggestions were mainly intended to illustrate the depth of changes that Twitter may need to consider to fix the noise (if it wants to do that). However, as I say, removing the retweet feature would somewhat enforce the opportunity to add value instead of mindlessly passing on material. Whether user would take this opportunity is of course another matter.
As you mention, the fix may ultimately come in the form of people migrating to another platform that is less casual/private than Facebook but keeps the noise better under control. In addition to the services you mention, I think LinkedIn is an interesting service to watch in this sense; they have been slowly developing social features and may yet emerge as the professional social networking platform.