Your hypothesis does not seem too crazy.
Hopefully we will be a transplanetary species by then and won't suffer much apart from some nostalgia.
The longest Earth can last is probably until the sun enters its white dwarf stage in 5 or so billion years. Unless a technology is built to protect it.
The most pessimistic predictions say Earth will explode in a nuclear war that could happen in a few decades thanks to North Korea or another dictatorship.