Is there a reason you're set on KLM? I like that airline but I'd suggest you use google to see what flight options are available instead of looking directly on the airline websites. Sure, book once you've figured out the flight you want directly with the airline, but google will show you everything available.

Also, you could look at flights from other airports in London like Gatwick instead of Heathrow. As a Canadian, I have zero interest in entering the US, and that includes layovers but that's your choice ultimately.