For this situation I think you really need a browser, unless anyone else can suggest alternative approaches.
But thats ok, we can now launch and control a browser using Zest :)
So I would write a Zest script that posts a test value, then launches the browser and opens the page that uses the GET request.
When you have that working you can surround that with a Loop which goes through one of the XSS attack fuzzing files we provide and use that as the attack.
I would just check the resulting pages manually to see if any of the attacks have broken out of your HTML context.
But we also have a DOM XSS fuzzing file that makes a call back to the ZAP API, so it should be possible to automate the detection if thats what you want.
Want to give that a try?
Just let me know if any of thats unclear or if you hit any problems and I'll help you sort it out.
I've done something similar fuzzing an application protected by a SSO solution which I demoed at AppSec EU:
https://www.youtube.com/watch?v=Ofmp-haNI7s from around 28:00
Cheers,
Simon