To make the heads-up notification stay there, you need to use
PendingIntent dummyIntent = PendingIntent.getActivity(context, 0, new Intent(), 0);
notification.setFullScreenIntent(dummyIntent, true);
My understanding from the post I got this from is that the app thinks it should keep it there until the full screen intent takes action, but it never will because it was a dummy intent.
https://stackoverflow.com/a/45516069/6296686
To update the notification use
notificationBuilder.setOnlyAlertOnce(true);
//Use the same builder when updating
notificationBuilder.setContentTitle("Updated Title");
notificationManager.notify(notificationID, notificationBuilder.build());
https://stackoverflow.com/a/15538209/6296686