I feel you man. We had to go through Barcelona-JFK to JFK-Seattle to Seattle-Victoria and it was absoltuely brutal. 8 hours + 6 hours + 1 hours (just flights!) and the wait at JFK alone was at least four hours. We could have skipped one stop for about $200 each and we will absolutely do that in the future. Going through another airport these days just isn't worth it, especially if it takes almost half a day and you still have to eat which costs a fortune in itself.
The way there was about 10.5 hour from Seattle to Germany and then another 1.5 hour to France (some time in between too, not exact) and because I can't sleep at all on flights I took a heavy sleeping pill on the way there and a few drinks on flight and still didn't sleep a wink. Luckily, for the second 1.5 hr flight I slept the entire way through so I was sort of rested when I had to rent a car in France (never Europcar ever!!!!) but it was still brutal.
The one thing I will say, no matter how messed up you think you will be 10+ hours after a sleeping pill it wont be half as bad as actually not sleeping while crossing the world. Nothing messes your body and mind up more than travelling across the world without a second of sleep. If you can, do whatever it takes to sleep on the plane and get your driviing/travelling when you arrive accommodated for you without doing any driving yourself.