The two preserved ones, Sharpthorne on the Bluebell Railway and Charwelton on the Kent and East Sussex Railway would make lovely examples.
The former I think is a K and has dumb buffers and was first used as a contractors loco on the Great Central, then used on building the Bluebell line itself.
The second may be an L.
There is of course the one the SE & CR had for use in Folkestone another K ?
This was bought by the SER, operated under the SE & CR in full Wainwright livery, then battleship grey, but unfortunately lost its chimney cap and looked a bit drab and dire. It was seconded to Hawkhurst during WW1 as station shunter, presumably during the hop-picking season, but was not successful.
Then the two on the Isle of Wight.
Freshwater, Yarmouth and Newport Railway K.
Bembridge branch BEMBRIDGE. possibly L.
From memory, this was called up for military service during WW1 and got sent to Mesopotamia.
I think that the K type had at least four cab options to choose from, ranging from just a basic front spectacle plate to fully enclosed.
That's a little bit to think about.
I wonder which type it will be ?