Question : Have you considered flying out of an airport besides London Gatwick Airport (LGW)?
Answer : Departing from London Gatwick Airport is not the only way to get to Chattanooga Airport. Try looking for flights from London Heathrow Airport (LHR) as well. Over the upcoming two months, flights from LHR to CHA are being booked 55% cheaper than flights from LGW to CHA. Being only 25 miles away, it's easily accessible for most.
Question : How long do most people visit Chattanooga?
Answer : Of course you're not most people, but if you were, you'd stay roughly 10 days.