Since you are already paying a lot for your electronic resources, why not also make them available via
When your patrons search Google Scholar, and find full-text articles in databases that you subscribe to, a link can appear in Google Scholar.
Flagler College has done a nice job of explaining what they did with some screenshots to boot.
Here is the info from the Google Scholar site about how to set up these "Library Links". There is no charge for participating in the Library Links program.