By "the joist" I meant the one that the old fitting was attached to. I doubt there are any more though tbh. The first room is a tiny cloakroom, barely 2m². The second isn't much bigger. Definitely not 6-8 joists to contend with! That said, I can identify any obstructions in as messy fashion as I like as I don't need to worry about the existing ceiling.You mention joist in the singular, you will have multiple joists up there.
At a rough guesstimate, you're likely to have somewhere between 6-8 joists to contend with (depending on the direction they run) from one wall to the other. This means that somewhere around 4 of these are going to be in your way. Not to mention noggins
One light either side of that joist would be sufficient, I'm only considering 4 purely for asthetics.