Just pondering at the moment really.

Does anybody have a 120mm spaced (track) fixed or single-speed bike that fancies adding a couple of extra gears?

I did this project last year. Managed to find a brand new Sturmey Archer 3-speed hub with quite narrow OLN spacing (about 112-114mm iirc). This hub is one of the original AW types made in England in the early eighties that had sat unused in its original packaging until I stumbled upon it.
The OLN spacing is important as it allows an extra set of captive washers to go on the inside of the dropouts; this hold the wheel very securely in the frame without having to use ugly chain tugs.
I laced it to a Mavic Cosmos rim that I had (less than 1000 road miles old), using DT SS double butted spokes.
I installed the 3-speed trigger on the drive side seat stay and it worked perfectly.
But I didn’t get around to riding it!
Then, on a whim, I converted the bike to flat bars; and still didn’t use it!
Done about 25miles at the most.

So, finding myself skint, I’m contemplating selling the wheel, shifter and parts.

Would there be any interest in such a beast?

I might be interested in the wheel for my commuter. Drop me a mail, if you see this.

Sturmey still make the 3speed hub has in 119, 117, 111 and 108mm OLD if you cannot find an NOS AW hub which last forevever.

There is also a 5 speed with OLD of 119 and 111mm

All true, yes. Production quality also tends to be a bit better after ownership transferred to Sunrace in 2001.