'ere's the deal: Junctions are dangerous places on the roads. Roundabouts are dangerous places because they are multiple junctions. Big roundabouts are even more dangerous. It doesn't matter whether you are on a bike, on foot, in a car. They are dangerous. You can adopt mitigating strategies all you like, but you have to realise that riding a roundabout has risk that you can't control. Drivers looking for exits, not looking at exits, looking at their phone, you name it. That was forcibly brought home to me a few years back when I was rear ended, doing about 20+, coming off Hyde Park Corner by a driver who just didn't see me. Fortunately, as the speed differential wasn't that great (and it must have been quite square to my rear) I just got pinged forward, but my trousers were definitely a little browner.
So, when cycling I ride car-like, and try to fit myself into the traffic flow, but as often as not I would try to avoid these days. And, if it was particularly nasty, I might even wuss out and cross as a ped, or a bike equivalent (stop on the left kerb before crossing when clear or stopped.