I think the only way to get from WLL to SWML would be via Point Pleasant Junction, East Putney and the District Line. This would obviously be completely unfeasable, unless you took over the district line South of East Putney, which would anger no end of District Line commuters from Wimbledon/Southfields.
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Wouldn't this be using the old Cross Country Brighton route, which went via Clapham Junction, Kensington Olympia and then via Mitre Bridge Junction, West London Junction and Acton Wells Junction. None of these are horribly sharp curves. (I'm not suggesting this is a good idea though, due to a lack of paths).
Route here.