Well yeah, screen scraping would be required. The core of the product would have to be a screen scraping engine that makes it easy to build screen scrapers fast. You'd also have to commit to daily updates of all the various screen scrapers to keep them working. Without that it would fail.
You could be a little bit more adversarial in the approach. Create several accounts, have them each message one another. Since you know the message and can use OCR, you can easily automate compensation for changes in the UI.
Perhaps a machine learning approach could work.