I like the idea of using a webhook. It was my initial approach to doing this. The biggest problem with using a webhook with a WordPress multisite installation is that it doesn’t return any data that will allow the updated Discourse topic to be matched with the correct WordPress subsite. For each webhook request, the postmeta table of each WordPress subsite will have to be searched to try to match the topic with a post. For a network with 100 subsites, this could become quite inefficient.
I’m going to give this some more thought and see if there’s a way to make it work.