I noticed the same issues that the vertical accordion menu expands fully and does not want to close unless I am on another page. Other than the sponsor page.
Also, the jquery interferes when another is called their script after yours. The other query that run a modal window(popup). This does not work unless I uninstall the sponsor plugin. Is there a way we can get a query fix to work together with others or is it a matter of relocation to be first on the list in the page creation.
I will try to add the query directly in the function php to establish it first in the header. Then see if other queries are in control when established after. If you have a better idea let me know. It may take some time for me to test unless you come up with a fix before then.
Otherwise, I would rate this a 5-star plugin and comment that it is very professional looking for any website. Sponsor should not have an issue with adding their logos.