Time for some sleep here, but I do have a simple Proof of Concept version that adds the original ?theme=2010 type of query to the end of every link on a page when the sticky setting is triggered. I have not yet added checks to be sure the link is on the current WordPress site, or that the URL does not already have a Query.
Nonetheless, I'll do some testing tomorrow and see how close I am to a Proof of Concept that you can try out.
I do hope that things go peacefully in the aftermath of your national election.