I don't know what download URL you are using, but it sure can't be from the v1 ReST API. You do not need store_type or store_id for the access to the node content aka "download". Only if you were to use the legacy APIs, like the download servlet, would you need to have those extra parameters.
I am little confused about the version I am currently using. If I try to use the URL as you specified, how alfresco would know where it saved? Will it get information from the document by id such as store type and store_id, and then get the content of the file? If you know its implementation and explain it here, I would be thankful