Accessing a web part's properties within a transformation can be a lot of work. If I understand your problem correctly, I may have a simpler solution.
Basically, you want your transformation to create a link to the document that is currently using the transformation to display some data. So instead of using GetDocumentUrl() which would get the URL of the list item, you want to get the URL of the document where the list is displayed, right?
This should do it:
GetAbsoluteUrl(GetUrl(CMSContext.CurrentDocument.NodeAliasPath, CMSContext.CurrentDocument.DocumentUrlPath), CMSContext.CurrentSite.SiteID)
This returns the URL to the current document and, obviously, the value will be the same for all rendered items. You can append your changing query string to this.