Anatoly Mironov has a great post on how to export web parts when the export functionality is disabled (like XsltListViewWebParts).
Find the full post here.
In summary:
Use the following url, changing the guid string with the web part id:
https://intranet.contoso.com/_vti_bin/exportwp.aspx?pageurl=https://intranet.contoso.com/Pages/default.aspx&guidstring=0c3adfe9-8f5d-4432-918a-42410e4e324d
where the web part id can be retrieved by looking at the source code, finding your web part, and looking for the:
<div webpartid="0c3adfe9-8f5d-4432-918a-42410e4e324d" ........ >