Amazing, thank you! Hadn't thought of doing it that way round (alarm to trigger relay for door) - I was digging round trying to find if there was a door receiver that could be used to trigger the alarm!
Will have a route round for the bits, then might have a better idea of specific Q's to ask (like "how do I make sure the alarm doesn't automatically arm if I just close the door" - but I need to know how many channels on the RF before I do that)! ?
I may as well dive in and do it properly (that way I'll get round to putting contact switches on the doors, rather than just relying on an interestingly placed PIR in the hall).