You do not need to call it asynchronous callbacks (believe me, it will become clearer ...).
ResponseStream will load as information becomes available. In the case of a small (for fairly large values ββof "small", I'm afraid) a thread that is not sent, this will be when the entire thread has been loaded. However, if a stream is sent with alternating transfer coding (this is what happens in ASP.NET, if buffering is disabled or Response.Flush() is called, other web server technologies have their equivalents), then the stream will be available on the first fragment.
Create your XMLReader from ResponseStream when returning GetResponse (). It will start processing from the first available fragment and will receive subsequent fragments, since they will be fairly transparent in your code.
Make sure that your access to these nodes in an affordable way really benefits the code further along the line. For instance. if you go to the console or to the form, do it the way each node (or a small batch of nodes) is processed, whereas if you create objects from these nodes, then yield return them instead of creating a collection.
Now, the big thing here, obviously, is that the web stream is fragmented, not your processing code. If the manufacturer is another side that cannot be convinced of this, then you will need to switch to a lower level of processing. However, if this is the case, then this is most likely a false optimization, since all processing will be performed at their end before sending the first byte, and this will be the biggest delay. Indeed, if the delay to receive the whole downloaded response is a problem for your code, then you need to start sending marked ones, since the delay with even the most efficient approach on your part will still be too large.
In this entry, I recently confirmed that with this use of XmlReader in WebResponse related to chunked data (where I controlled the client and server code and could work both in the debugger and check the order of work), the processing is really performed, since each piece is available .