Had a chat with my parents tonight, they're both really keen on the idea! Mum was all along, but Dad was a bit uncertain, thought it'd be too much bother. He's a bit of a handyman though, and is really excited with the idea of helping build a coop out of this BBQ. He went looking through all the scrap metal etc around the place and helped come up with a design for it. It's going to have corrugated sheet steel sides and roof now, he's got a big roll of that lying around. The nesting box on one end will be the only wood we'll need to buy (marine grade ply). It will have an openable lid for easy access.
Will definitely take before/after and progress photos when we get to work (probably won't be til after Easter).