pstock

I am trying to get my wife's recently acquired Bike Friday up to speed.
I got it third hand and so there are some odd bits to it.

When acquired last week it was set up like this:
Shimano 600 RD.
Internal 3S rear hub (heavy but obviates the need for a FD)
7S rear Shimano Hyperglide cassette.

But, oddly, it had Campy Daytona brifters. (and when I tested the RH brifter it was a 9S so evidently the previous owner had been I presume throttled it back to 7S with the limit screws. I am surprised it would even shift cleanly with a 9S brifter.)

the bike apparently dates from 2009, so the 7S rear cassette befuddles me.

my first thought was to just swap it out for at least 8S.

however, my 8S Shimano cassettes, while they fit the splines on the body, stand out one cog too proud. the 8th cog doesn't grab and I cannot lock it on.

can anyone
A) ID this rear hub? (it might be a generic Sachs knockoff)
but more importantly
B) advise me on what kind of cassette this requires.
were 7S bodies incompatible with 8S cassettes?

thinking maybe that there was a spacer knocking out the 8th cog, I removed the large flange you see in the series of photos. But, I think in retrospect that is more of a dust cover than a spacer (as I can see the ball bearings in the hub when it is removed.)

many thanks as always.

Peter