Is there a way to use a query string parameter to override sticky sessions?

Sorry, I was trying to be humorous. What I meant was you could use iRules to meet your needs. Considering what you are looking for I wouldn't want to even try and code such a rule but it's certainly possible.

See here for an introduction to iRules: https://devcentral.f5.com/articles/-the101-irules-101-introduction-to-programming-amp-tcl.