That sounds like an awesome idea, actually the data is stored for every user separately depending on the used api token or when you login and do a data import. I will create a feature request for it.
But bear in mind, reitti is not meant to be a real-time tracking app. At the moment, data is processed every 10 minutes.
Let me know how it works out for you. If you have the gpx files, you can simply import them inside the settings menu.