The problem with the Clapham route is simply time. If you have the time then there’s money to be saved as described but expect to sit on an Overground train for a bit before departure. I’ve only tried it a couple of times but due to scheduling I had about a 10 minute wait for departure (and the South London line doesn’t seem to be the fastest bit of track around.)
In reverse, the issue may be fitting onto the return train to Strawberry Hill. My journey is on the Epsom line and we have half the service we had pre-COVID so getting onto the train on a mid-week evening is a squeeze. For that reason alone, I tend to opt for a Waterloo change rather than anywhere else. That may not be a problem on your line of course.
With the W&C it’s the popularity and thus the crowds that may be an issue. I’ve only tried it post-COVID and it’s manageable if not completely stress free. Pre-COVID I suspect it was a nightmare. It probably is the fastest route, though, rather than running via Vauxhall and joining the crowds on platform 8 on the return journey.
I can’t advise anything extra as to cost since Mike knows much more than me and my payment mechanism is different.