Replacing artificial background with sky

[PhilM]

Hi everyone,

This image is from Pendon Museum:


You can see that the model in the foreground is beautiful but the background is the room's ceiling. I want to replace that ceiling with an overcast sky image to match the lighting of the model.

The problem is how to do that as automatically as possible without hand-painting all the fiddly edges where "sky" meets model - especially behind the trees!

I've been playing with the colour selection feature in the Photo tool but without much success.

Do you have any tips or suggestions about the least painful way to do it?