Fetching it as one call would probably be useless even if you set the timeout high enough to capture all as the use will not get any feedback until its finished.
Going with multiple status polls is the only way to go.
But depending on how your server runs there might be some quirks to think of.
For example, IIS uses only one thread per session, so two simultaneous calls from the same client will be handled after each other.
If you have posted something with ajax or iframe that takes time to process, like a file upload, then that call will block the session and any status page need to be sessionless to be able to respond directly.