To simplify a rather large/complicated journey, we'd like to split it up into 4 mini journeys, with contacts who exit one journey a certain way automatically moving to the next journey. Is the way to do this the "Update Contact" option, or is there something else?
Update Contact can indeed be used to build kind of journey linking/orchestration. You should have a Data Extension which keeps track on your contacts entering and exiting journeys, and query this to build an entry audience for one of your subsequent journeys. However, as you might have realised this is not a real time link, and you will only inject contacts as a result of an automation run.
If you need a real time link, you will need to develop a custom Journey Builder activity, which calls the API trigger of the subsequent journey. Mind you, this only works if the journey you are linking to has the API entry event and not e.g. Salesforce Data entry event.
Both solutions have a drawback of not linking the contacts to the next journey if contacts exit the previous journey abruptly - e.g. due to exit criteria or goal being met. Here they will never pass through the Update Contact or your custom activity.