You can display the sponsor widget on the inner pages with a plugin named ”amr shortcode any widget”
Please have a look at
https://wordpress.org/plugins/amr-shortcode-any-widget/installation/
After adding the widget to the shortcodes sidebar, go to the edit screen of the page:
[do_widget “Tyler Sponsor List”]
While we do not endorse the use of external plugins, this extension could help solving the problem.