Just as a follow up to my own post...
I ordered a new 70-300 but it was decentered so it went back. Where it was sharp it was good, but not consistent across the frame. If my experience is typical, I can understand why the reviews of it are all over the place!
I then ordered a 70-200 f4 used from MPB. It's a really excellent performer. I can't understand why there are a lot of reviewers who say it lacks resolution. In my experience, it's pretty damn sharp right across the frame, even at f4. In fact, telling shots at f4 and f8 apart is easiest by looking at the vignetting rather than the sharpness.
But ... it's a pretty big and heavy lens so I'm not sure I'll keep it.
There are rumours of a new 28-200 or 24-200. If Panasonic deliver something like the Tamron 28-200 then I'll be very happy. No dates yet of course.
So, once again I'm finding that FF is nice and all, but once you get past 100mm, the size and weight of the lenses starts to be an issue. I think I'll stick with the S5, but I'll need to compromise on reach. I do mostly landscapes, so the 24-105 I have now should cope with most things, but I'm sure I'll miss something longer from time to time.