Thanks for the input and sorry I didn't reply earlier, I was only notified of the first reply.
So Garmin did get back to me and after initially failing to properly read my question replied with an extract from the manual where "calibrate using pressure" is mentioned... in a follow up they admitted that "Unfortunately there is no other way to calibrate the pressure on the device.". A rather neglectful omission if you ask me considering my Avocet Vertech from 1995 can be adjusted!
So you're stuck with either a wrong altitude/correct QNH pressure or a correct altitude/wrong QNH pressure. Since trends are what's important here you can live with a wrong QNH pressure but still, it's annoying and it shouldn't have to be like that.