Definitely dreaming.... but what I have always wondered is how does New
York manage to run a 24-hour service, or is this because they can often
re-route trains if they want to close a section of line (very muddling
for visitors!), which we can't do in London?

It's partly because of the ease of reroutes (yes, including, but not
restricted to, the 3 and 4 track sections) and partly because they
don't have a legal requirement to walk every inch of track at night.
They also have the advantage of not having a 4th Rail, so it's safe
for MOW to walk along the 4 foot.