Ok, some progress.
I debated keeping the 'too big' base as is, and putting some damp proof membrane onto it, but in the end decided to correct it. It took me from early morning to 3pm to move the walls, remove the floor, cut the joists, re-level and put everything back. I'm glad I did it though, it would have nagged at me every time I saw it.
We're in the middle of an unusually long dry spell for September here in the UK, so the lack of a roof hasn't been an issue. Unfortunately, I'm back at work after some hols, and shed work is limited to an hour or so a day.
'Moving in' was a milestone. It was going to be easier to get the workbench through the wall space rather than the door, so I did that before continuing:

And I've since started the roof framing (so I could get a tarp up there properly in case of rain) and continued with the final wall.

When the walls and roof are done, I can work inside the shed at my own pace, finishing the windows and doors. Hopefully I'll be able to crack on with that this weekend.