Thanks and yes, I'd read through a few threads about Chromecast Integration, though most of them seemed to be 'not working at all' or 'messages only sometimes getting through'. I was hoping that because it is working 100% with the Home Minis and 0% with the Nest Minis that it might just be something I needed to change in Hubitat.
After a Github/Hubitat newbie-error (I was looking in drivers rather than apps) I installed Chromecast Helper by the fantastic @bptworld. That appears to have fixed the issue and now both Home and Nest are working. Thank you @bptworld