Transwikification does not require administrator privileges. One doesn't even need an account in order to transwikify articles. The thing about transwikification is not that it requires privileges, but that it is a lengthy procedure. One has to edit four separate pages for each article transwikified, and do a lot of tedious copying and formatting of edit histories. There are several GFDL-mandated details that it is easy to miss. This is why several editors have written various semi-automatic tools that will handle all of the detailed rote work involved.
And those are just the raw technicalities of copying the articles in a GFDL-compliant way. There are other considerations as well, such as dealing with the article on the target project. There's a tag that should be applied to every article transwikified into the Wikibooks Cookbook, for example.
But the actual transwikification of articles is not the whole story. There are other, simpler, things that you can help out with: