I forgot to mention this one - the door lock (which came with the least useful instructions every seen!) came with a mysterious small blue electrical component. However, a bit of Googling found this page which not only explained what the impact of back EMF is with magnetic door locks, but also why a diode (which I'd have probably used myself, not knowing better) isn't a very good solution for them as it can result in the lock getting stuck, or being slow to release. Fortunately, that page mentions MOVs (metal oxide varistors) as the correct way to consume the back EMF from the coil, and even has a nice picture of the exact, mysterious component that was in my box so it solved two problems in one.1. Back EMF from the lock might upset the alarm.
In the end, I wired it to isolate both connections to the coil through my relay (mostly as this made it much easier to locate the MOV in the panel), so I think the combination of the two should avoid any unexpected PSU zapping.