Bonernow,
I would tell them that, given your 767 experience, you want 777 or no deal. Simple as that. I have heard the A320 fleet is a nightmare (just read the last 300 pages of this thread). You have flown heavy Boeings and you want to fly heavy Boeings - or no deal. Hold firm and tell them you will wait for the next Boeing class or just pass... Other carriers in the region are hiring.
Sounds like if you want to fly the 787 at QR down the line, you need to be a Boeing driver.